2025​​Activity reportProject-TeamQINFO​​​‌

3.1.1​‌ Efficient methods for testing​​ and characterizing quantum systems​​​‌

Obtaining an accurate mathematical​ characterization of the quantum​‌ systems that are prepared​​ in the lab is​​​‌ a pressing question for​ quantum technologies. For this​‌ reason, there has been​​ very important progress on​​​‌ such statistical questions in​ the last few years.​‌ This includes the answer​​ to foundational questions such​​​‌ as the number of​ samples needed to characterize​‌ an unknown quantum state,​​ improved methods for characterizing​​​‌ quantum devices, and very​ recently techniques that can​‌ very efficiently predict multiple​​ relevant properties of quantum​​​‌ systems. We plan to​ contribute to these lines​‌ of work by considering​​ several questions all going​​​‌ in the direction of​ better characterization of quantum​‌ systems.

First, we will​​ consider basic statistical questions​​​‌ related to testing relevant​ properties of quantum states.​‌ In particular, given a​​ description of an ideal​​​‌ target state $|\mathrm{\psi }\rangle$, how to​‌ efficiently test whether the​​ state prepared by the​​​‌ device complies with $|\psi \rangle$? Another​‌ question is how to​​ test whether the state​​​‌ prepared by the device​ is entangled or not?​‌ These are fundamental questions​​ and for some of​​​‌ them the best known​ algorithm is to learn​‌ the whole state by​​ performing a complete quantum​​​‌ tomography. We believe that​ this is far from​‌ optimal and that a​​ better understanding of the​​​‌ geometry of quantum states​ can be turned into​‌ a significantly more efficient​​ testing algorithm. Techniques from​​​‌ high-dimensional convex geometry 60​ are likely to play​‌ an important role.

Building​​ on that, we will​​​‌ then develop tools to​ characterize the noise affecting​‌ quantum devices. As the​​ number of parameters and​​​‌ samples required to characterize​ an arbitrary noisy process​‌ grows exponentially in the​​ number of qubits 95​​​‌, it is of​ paramount importance to devise​‌ protocols to find an​​ effective ansatz for the​​​‌ underlying structure. The first​ step we will take​‌ in this direction will​​ be to devise scalable​​​‌ protocols that are able​ to identify the correlation​‌ structure of the noise​​. By singling out​​​‌ on which parts of​ the device the noise​‌ acts independently and on​​ which the noise is​​​‌ correlated it is possible​ to substantially reduce the​‌ number of parameters that​​ are required to effectively​​​‌ describe it, bringing it​ to a tractable number.​‌ Although finding the conditional​​ independence structure of a​​​‌ set of random variables​ to a high precision​‌ is a difficult problem​​ even classically, we will​​​‌ generalize to the quantum​ setting efficient classical techniques​‌ that employ convex relaxations​​ 76 to obtain good​​​‌ approximate solutions.

The next​ step will then be​‌ to devise protocols inspired​​ from machine learning techniques​​ that can exploit the​​​‌ knowledge of the underlying‌ correlation structure to efficiently‌​‌ learn its parameters. This​​ will be combined with​​​‌ randomized benchmarking techniques 86‌, 90, 84‌​‌. Randomized benchmarking techniques​​ are known to be​​​‌ robust and experimentally friendly,‌ however current results either‌​‌ give very limited information​​ or require stringent assumptions​​​‌ on the structure of‌ the underlying noise. Thus,‌​‌ the goal of this​​ part will be to​​​‌ overcome these two limitations,‌ providing experimentalists with much‌​‌ needed tools to efficiently​​ characterize large noisy quantum​​​‌ devices.

Such a line‌ of research certainly also‌​‌ profits from inputs from​​ experimentalists to test the​​​‌ algorithms on real quantum‌ hardware. Thus, we‌​‌ plan to work with​​ the local experimental group​​​‌ led by Benjamin Huard‌ to test such methods‌​‌ on the devices they​​ build. Moreover, it is​​​‌ invaluable to obtain input‌ from experimentalists regarding what‌​‌ are the limitations and​​ challenges they face in​​​‌ the lab when characterizing‌ their devices.

An important‌​‌ aspect in this direction​​ that we will consider​​​‌ is the design of‌ measurements that can probe‌​‌ the physical property of​​ interest without disturbing the​​​‌ state by much. This‌ is the so-called quantum‌​‌ non-demolition measurement (QND) and​​ is important when one​​​‌ has a continuous signal‌ which one wants to‌​‌ measure, since one has​​ to measure the same​​​‌ system repeatedly over time‌ and, ideally, one wants‌​‌ the outcomes of later​​ measurements to depend solely​​​‌ on the quantity one‌ intends to measure, and‌​‌ not on any disturbances​​ caused by prior measurements.​​​‌ QNDs have found usages‌ in many areas, including‌​‌ quantum computing and, most​​ prominently, proposals for gravitational​​​‌ wave detectors with improved‌ sensitivity. We view the‌​‌ problem through the lens​​ of quantum information theory,​​​‌ and in this way,‌ it can be seen‌​‌ that the quantum system​​ involved in the QND,​​​‌ is a quantum reference‌ frame. What’s more, there‌​‌ is a one-to-one relation​​ between the reference frame​​​‌ imperfections, and its ability‌ to act as a‌​‌ system for QND measurements.​​ In 64, 112​​​‌, we gave a‌ construction of a QND‌​‌ where the error is​​ a function of energy​​​‌ and dimension. Going forward,‌ our objective is to‌​‌ determine whether this construction​​ is optimal, determine the​​​‌ optimal tradeoff between error‌ and energy and dimension‌​‌ and assess the extent​​ to which such constructions​​​‌ can lead to an‌ advantage for quantum sensing‌​‌.

3.1.2 Limitations on​​ the computational power of​​​‌ noisy quantum devices

In‌ order to establish a‌​‌ quantum advantage for noisy​​ quantum computers, it is​​​‌ important to study when‌ noisy quantum computers can‌​‌ be simulated classically.​​ Intuitively, it is clear​​​‌ that the noise present‌ in a quantum device‌​‌ imposes a limit on​​ the circuit depth we​​​‌ can implement before the‌ device loses its usefulness‌​‌ when compared to classical​​ devices. In order to​​​‌ understand the potential of‌ noisy quantum devices, it‌​‌ is crucial to develop​​ tools to characterize when​​​‌ this happens given a‌ problem and noise model.‌​‌ In the context of​​​‌ optimization, such bounds were​ achieved by our work​‌ 85. In short,​​ the results of 85​​​‌ show that sampling from​ the output of noisy​‌ quantum devices quickly becomes​​ comparable to sampling from​​​‌ Gibbs states that are​ easy to simulate classically​‌ by giving stringent explicit​​ bounds. This is showcased​​​‌ in Figure 1,​ where we plot at​‌ which density of corrupted​​ qubits the noisy quantum​​​‌ device loses advantage against​ classical methods.

Estimate as​‌ to when a noisy​​ quantum device loses advantage​​​‌ compared to established efficient​ classical methods in terms​‌ of the density of​​ uncorrupted qubits for one​​​‌ instance of the GSET​ (a set of instances​‌ of hard combinatorial optimization​​ problems that are used​​​‌ to benchmark solvers). We​ see that even when​‌ only a fraction of​​ the qubits have been​​​‌ corrupted (roughly one in​ 4), the noisy quantum​‌ computer is already expected​​ to lose advantage against​​​‌ heuristic methods.

However, in their​ current version, our methods​‌ only allow for an​​ analysis of the first​​​‌ moments. To extend the​ analysis and conclusions beyond​‌ optimization to other fields​​ like quantum machine learning,​​​‌ it is imperative to​ obtain results for higher​‌ moments and concentration inequalities​​ for the outputs of​​​‌ noisy quantum circuits. That​ is, to quantify how​‌ much noise a quantum​​ system can tolerate before​​​‌ it behaves like a​ state that can be​‌ easily sampled from classically.​​ To achieve this goal,​​​‌ we intend to resort​ to and further develop​‌ methods from the emerging​​ field of quantum optimal​​​‌ transport 100, 77​. Optimal transport techniques​‌ are by now a​​ well-established method to show​​​‌ powerful concentration inequalities 105​. They are known​‌ to combine well with​​ other areas of expertise​​​‌ of the group, such​ as entropic and semigroup​‌ methods.

3.1.3 Efficient optimization​​ using noisy quantum computers​​​‌

Identifying good use cases​ for the noisy quantum​‌ devices expected to be​​ available in the near​​​‌ future is one of​ the main current challenges​‌ faced by the quantum​​ computing community. One possible​​​‌ candidate for such an​ application are quantum Gibbs​‌ state-sampling based methods. Quantum​​ Gibbs states are at​​​‌ the core of powerful​ classical and quantum algorithms​‌ for optimization and machine​​ learning based on mirror​​​‌ descent or the matrix​ multiplicative weight method 69​‌, 66, 65​​. These iterative algorithms​​​‌ can be understood as​ a variation of simulated​‌ annealing, in which one​​ starts with a (quantum)​​​‌ Gibbs state at infinite​ temperature and decreases the​‌ temperature to converge to​​ the solution of an​​ optimization problem. That is,​​​‌ we begin with a‌ state that is supported‌​‌ everywhere on the state​​ space and slowly zoom​​​‌ into regions that contain‌ solutions to the problem‌​‌ of interest by tuning​​ the Gibbs state. This​​​‌ intuitive picture conveys one‌ feature of such methods:‌​‌ they are robust, especially​​ at the first iterations,​​​‌ as we only need‌ to ensure that we‌​‌ are zooming in the​​ right direction. This robustness​​​‌ translates into them only‌ requiring the preparation of‌​‌ states with relatively small​​ precision to make progress.​​​‌

On the other hand,‌ this picture also showcases‌​‌ the issue noise imposes​​ for such methods: after​​​‌ a while, the noise‌ will make it impossible‌​‌ to zoom in further,​​ imposing fundamental barriers onto​​​‌ how well we can‌ characterize the region of‌​‌ solutions. Thus, it is​​ expected that noisy quantum​​​‌ computers can offer useful‌ advice as to which‌​‌ direction to go up​​ to a level that​​​‌ naturally depends on the‌ noise present in the‌​‌ device. Thus, we will​​ design hybrid quantum-classical algorithms​​​‌ that explicitly take into‌ account this limitation. They‌​‌ will only use the​​ quantum computer to identify​​​‌ a region of a‌ relatively small dimension that‌​‌ contains the solution.

At​​ this stage, it is​​​‌ then possible to use‌ powerful randomized linear algebra‌​‌ techniques to take advantage​​ of the initial zooming​​​‌ in performed by the‌ noisy quantum device. Techniques‌​‌ from randomized linear algebra​​ offer significant speedups for​​​‌ basic operations under the‌ promise that the involved‌​‌ matrices are supported on​​ a small dimensional space​​​‌ 110. Thus, after‌ doing the first iterations‌​‌ efficiently on the noisy​​ quantum device and identifying​​​‌ a low-dimensional space that‌ contains the solutions, a‌​‌ classical device takes over​​ with this input and​​​‌ runs the later iterations‌ much faster. Such a‌​‌ hybrid algorithm would lead​​ to more efficient solvers​​​‌ for convex optimization problems.‌ Although such problems can‌​‌ usually be solved in​​ polynomial time, in practice​​​‌ it is still challenging‌ to solve larger dimensional‌​‌ instances, impeding their more​​ widespread use. Such a​​​‌ hybrid algorithm will increase‌ the practicality of solving‌​‌ large-dimensional semidefinite programs, as​​ the classical computer would​​​‌ only have to operate‌ in the low-dimensional regime.‌​‌ It would also lead​​ to provable speedups for​​​‌ quantum devices under noise,‌ a goal that has‌​‌ so far remained elusive.​​

The main technical challenges​​​‌ that need to be‌ overcome for the success‌​‌ of such an algorithm​​ are threefold: first, carrying​​​‌ out a detailed analysis‌ of the trade-offs as‌​‌ to when it becomes​​ more efficient to transition​​​‌ from performing the optimization‌ on the noisy quantum‌​‌ device to the classical​​ computer. Second, the development​​​‌ of improved quantum Gibbs‌ sampler for noisy devices‌​‌ to prepare the required​​ states. Third, the identification​​​‌ of practically relevant problems‌ that offer a good‌​‌ opportunity window for quantum​​ speedups. The first and​​​‌ third challenges will profit‌ from and are connected‌​‌ to the result of​​ the previously discussed Goals​​​‌ 3.1.1 and 3.1.2.‌ The second, the development‌​‌ of better quantum Gibbs​​​‌ samplers, as current proposals​ for Gibbs samplers require​‌ quantum circuits that are​​ unlikely to be implementable​​​‌ in the near term,​ will certainly yield results​‌ that find applications in​​ many other directions. Indeed,​​​‌ efficient classical Gibbs samplers​ are the bread the​‌ butter of most Monte​​ Carlo techniques, and it​​​‌ is to be expected​ that quantum Gibbs samplers​‌ will find similar widespread​​ application.

3.1.4 Certification of​​​‌ quantum devices

In the​ device-independent framework of quantum​‌ cryptography, protocols offer security​​ by relying on minimal​​​‌ assumptions. Namely, they are​ secure even when the​‌ devices used within the​​ protocol are completely untrusted​​​‌ or uncharacterized. The main​ idea behind many device-independent​‌ protocols, such as randomness​​ expansion and quantum key​​​‌ distribution, is that there​ are certain correlations between​‌ multiple separate systems that​​ ($i$) could​​​‌ only have been produced​ by entangled quantum systems​‌ and $\left(i\mathrm{i}\right)$ are intrinsically random.​​​‌ The fundamental question underlying​ the analysis of such​‌ protocols is how to​​ certify entanglement or randomness​​​‌ from the observed measurement​ statistics of the untrusted​‌ device?

This question of​​ certification is recurrent when​​​‌ assessing the behaviour of​ quantum devices (and particularly​‌ of noisy ones), as​​ highlighted by the issues​​​‌ that Goals 3.1.1 and​ 3.1.2 address. We plan​‌ to develop techniques to​​ address the certification of​​​‌ quantum systems with minimal​ assumptions. Our objective is​‌ to first build mathematical​​ tools in the continuity​​​‌ of the Entropy Accumulation​ Theorem 79 that allow​‌ us to make accurate​​ statistical statements about large​​​‌ quantum systems. The second​ objective is to design​‌ computational methods 68 to​​ certify in a quantitative​​​‌ way the relevant quantum​ properties that are consistent​‌ with the observed statistics.​​

For the context of​​​‌ device-independent cryptography, this will​ allow us to obtain​‌ protocols with improved noise​​ tolerance and finite-length analysis​​​‌ to reach the realm​ of what can be​‌ done with current quantum​​ technologies. But we believe​​​‌ these techniques will be​ applicable in the wider​‌ setting of certifying properties​​ of quantum networks and​​​‌ quantum computing devices.​

3.2.1 Optimal error correction​ tailored to noise model​‌

Shannon's 1948 seminal theorem​​ 102 modeled the problem​​​‌ of communication (or storage)​ over a given noisy​‌ channel and determined precisely​​ its ultimate limit. Shannon's​​​‌ noisy coding theorem relates​ the maximum rate at​‌ which information can be​​ transmitted reliably over a​​ noisy channel ${𝒲}_{\mathrm{X‌}\to Y}$ to a‌ simple entropic expression $\mathrm{I‌‌}(X:\mathrm{Y})$ measuring the correlations​​​‌ between the input and‌ output of the channel.‌​‌ More precisely, it states​​ that as $n\to ‌\infty$, the maximum‌ number of bits that‌​‌ can be sent using​​ $n$ independent copies of​​​‌ ${𝒲}_{X\to \mathrm{Y‌}}$ is asymptotically given by‌​‌

where the right‌​‌ hand side is a​​ maximization over distributions ${\mathrm{P‌}}_X$ over the input‌ of the channel and‌​‌ $I(X:Y)$ is a​​​‌ correlation measure, the exact‌ definition of which we‌​‌ will omit in this​​ document. Setting the fundamental​​​‌ limits for reliable communication,‌ Shannon's theorem was instrumental‌​‌ in the discovery of​​ good error correcting codes​​​‌ which are used in‌ virtually every device or‌​‌ communication link today. One​​ of the goals of​​​‌ the field of information‌ theory is to characterize‌​‌ the optimal communication rates​​ in the form (​​​‌1) for various‌ information processing tasks.

Devices‌​‌ that make use of​​ the laws of quantum​​​‌ theory are also affected‌ by noise, in fact‌​‌ even more so. Determining​​ the optimal method in​​​‌ order to communicate (or‌ store information) reliably over‌​‌ a noisy quantum channel​​ is thus of fundamental​​​‌ importance in order to‌ exploit the full potential‌​‌ of a quantum computer,​​ or more generally a​​​‌ quantum device. However, despite‌ the problem's importance and‌​‌ more than 40 years​​ of efforts in quantum​​​‌ information theory 92,‌ 109, it is‌​‌ fair to say that​​ we do not have​​​‌ a quantum analogue of‌ Shannon's theorem Eq. (‌​‌1). Indeed, a​​ formula analogous to Eq.​​​‌ (1) for‌ quantum channels is known‌​‌ only in very special​​ cases. As an illustration,​​​‌ even for the simplest‌ possible quantum channel, called‌​‌ the qubit depolarizing channel,​​ the asymptotic maximum rate​​​‌ of quantum communication is‌ still unknown 78.‌​‌ The qubit depolarizing channel​​ can be thought of​​​‌ as the quantum analogue‌ of the channel that‌​‌ flips the input bit​​ with some probability $\mathrm{f‌}$.

The main difficulty‌ in understanding the ability‌​‌ of a quantum channel​​ in transmitting information is​​​‌ the non-additivity of the‌ quantum entropic quantities having‌​‌ the form of the​​ right hand side of​​​‌ Eq. (1)‌ 78, 93,‌​‌ 91, 103.​​ This challenge is due​​​‌ in many cases to‌ the quantum property of‌​‌ entanglement and we believe​​ that a new approach​​​‌ is needed to overcome‌ this difficulty.

Faced with‌​‌ these difficulties, we propose​​ a new framework for​​​‌ studying communication over noisy‌ channels. Instead of trying‌​‌ to determine the optimal​​ rate of communication asymptotically​​​‌ as the number of‌ channel uses $n\to ‌‌\infty$ (as in the​​ left hand side of​​​‌ Eq. (1)),‌ we assume we have‌​‌ a description of a​​​‌ finite channel ${\stackrel{¯}{𝒲}}_{\overline{X}\to \overline{\mathrm{Y‌}}}$ (a particular case​​ of which is ${\overline{\mathrm{𝒲‌}}}_{\overline{X}\to \overline{Y}}={\mathrm{𝒲‌}}_{X\to Y}^{\otimes n}$ for some finite​​​‌ $n$, but it​ could be much more​‌ general). Our objective is​​ then to design an​​​‌ efficient algorithm that determines​ the maximum number of​‌ bits or qubits that​​ can be sent reliably​​​‌ using ${\overline{𝒲}}_{\overline{\mathrm{X}}\to \stackrel{¯‌}{Y}}$.

For the problem​​ of classical communication over​​​‌ a classical channel, we​ have characterized this computational​‌ complexity precisely in our​​ previous work 63 and​​​‌ this led to interesting​ connections between information theory​‌ and combinatorial optimization. The​​ main objective here is​​​‌ to extend this approach​ to quantum channels, thereby​‌ designing algorithms that can​​ find the best error​​​‌ correction schemes for a​ given noise model.​‌ These algorithms can naturally​​ then be used on​​​‌ the noise models that​ are estimated using the​‌ methods developed in Axis​​ 3.1.1. In particular,​​​‌ we will focus on​ relevant noise models that​‌ appear in current devices.​​ For this we plan​​​‌ to collaborate with Benjamin​ Huard in the physics​‌ lab of ENS Lyon,​​ and the presence of​​​‌ Cyril Élouard in the​ team significantly helps in​‌ this regard. To start​​ in this direction, Cyril​​​‌ has given talks within​ the group to explain​‌ the mathematics of superconducting​​ qubits and we are​​​‌ at the moment discussing​ specific dissipative models that​‌ can be reasonably implemented​​ in hardware and for​​​‌ such different models compare​ their ability to store​‌ quantum information reliably.

3.2.2​​ Error correction and fault-tolerance​​​‌ with LDPC codes

Having​ a coding strategy for​‌ a given noise model​​ with good performance is​​​‌ not enough: for a​ strategy to be applicable,​‌ it is important to​​ be able to implement​​​‌ the error correction operations​ efficiently. An efficient decoding​‌ algorithm is not only​​ important to establish fast​​​‌ and reliable communication networks​ but it is also​‌ crucial for fault-tolerant computing.​​ In fact, the basic​​​‌ idea of fault-tolerant computing​ schemes is to perform​‌ computations on data encoded​​ in an error correcting​​​‌ code. To prevent the​ errors that occurred during​‌ the computation from spreading,​​ a decoding operation has​​​‌ to be regularly applied​ to correct these errors.​‌ For this reason, it​​ is crucial for the​​​‌ decoding operation to be​ very fast to prevent​‌ the accumulation of errors.​​ We focus here on​​​‌ an important class of​ quantum error correcting codes​‌ called Low-Density Parity-Check (LDPC)​​ codes 70, 104​​​‌ defined by two sparse​ binary parity-check matrices ${\mathrm{H‌}}_X$ and $H_{\mathrm{Z}}$ satisfying $H_X{\mathrm{H‌}}_Z^T=\mathrm{0}$. Our first objective​‌ is to design efficient​​ decoding algorithms for quantum​​​‌ LDPC codes.

Quantum​ LDPC codes are particularly​‌ well suited to achieve​​ fault-tolerant quantum computation. This​​​‌ is because the sparsity​ of the parity check​‌ matrices allows us to​​ bound the error rate​​​‌ of the syndrome measurements.​ In fact, currently the​‌ leading candidate error correcting​​ code to be used​​ in future quantum computers​​​‌ is the surface code,‌ a special kind of‌​‌ LDPC code. Even though​​ the surface code can​​​‌ be embedded on a‌ surface with only nearest‌​‌ neighbour interactions, it suffers​​ from a very poor​​​‌ encoding rate, and thus‌ using it for fault-tolerant‌​‌ constructions incurs a very​​ large memory overhead. Our​​​‌ previous work 83 shows‌ that in principle the‌​‌ memory overhead can be​​ significantly reduced by using​​​‌ constant-rate LDPC codes based‌ on expander graphs. The‌​‌ general idea of using​​ constant-rate codes is illustrated​​​‌ in Figure 2.‌ Our objective is to‌​‌ make fault-tolerant constructions with​​ LDPC codes practical by​​​‌ finding fault-tolerant gadgets for‌ such codes and using‌​‌ decoding algorithms with better​​ performance.

When using the​​​‌ surface code for fault-tolerance,‌ each qubit of the‌​‌ original circuit is encoded​​ in a separate block,​​​‌ leading to a large‌ memory overhead. When using‌​‌ constant-rate codes, all the​​ qubits of the original​​​‌ circuit are encoded in‌ the same block which‌​‌ leads to important savings​​ in terms of overhead.​​​‌

3.2.3 New‌​‌ approaches for fault-tolerance

As​​ mentioned before, the currently​​​‌ leading approach for fault-tolerance‌ is using surface codes.‌​‌ In contrast to the​​ previous goal 3.2.2,​​​‌ our objective here is‌ to explore radically different‌​‌ approaches to fault-tolerance that​​ could provide new avenues​​​‌ towards achieving fault-tolerance. In‌ particular, we will look‌​‌ at one based on​​ quantum polar codes and​​​‌ the other one based‌ on quantum reference frames.‌​‌

The class of quantum​​ polar codes that has​​​‌ recently been proposed in‌ 80 can be promising‌​‌ candidates for fault-tolerant quantum​​ computing. The construction relies​​​‌ on a channel combining‌ and splitting procedure, where‌​‌ a two-qubit gate randomly​​ chosen from the Clifford​​​‌ group is used to‌ combine two single-qubit channels.‌​‌ Applied recursively, this procedure​​ allows synthesizing a set​​​‌ of so-called virtual channels‌ from several instances of‌​‌ the quantum channel. When​​ the code length goes​​​‌ to infinity, the virtual‌ channels polarize, in the‌​‌ sense that they tend​​ to become either noiseless​​​‌ or completely noisy. Interestingly,‌ polar codes feature several‌​‌ extremely desirable properties: they​​ protect a high number​​​‌ of logical qubits, and‌ they have efficient decoding‌​‌ algorithms. In addition, logical​​ Clifford operations can be​​​‌ easily performed by using‌ code deformation like techniques.‌​‌ However, there are a​​ number of challenging issues​​​‌ to be addressed in‌ the fault-tolerant computing context.‌​‌ First, quantum channel polarization​​ needs to be investigated​​​‌ by taking into account‌ the fact that Clifford‌​‌ gates used for channel-combining​​ are faulty. Second, we​​​‌ need to construct a‌ universal set of fault-tolerant‌​‌ gates, which can be​​ tackled by using magic​​​‌ state distillation. For this‌ approach, we plan to‌​‌ collaborate closely with Mehdi​​​‌ Mhalla (CNRS, LIG).

The​ second approach we consider​‌ here is based on​​ a way of circumventing​​​‌ the famous Eastin-Knill theorem​. In the early​‌ days of quantum computing,​​ one of the key​​​‌ ideas for building a​ quantum computer whose errors​‌ can be corrected, was​​ the notion of transversal​​​‌ logic gates. The idea​ was to devise a​‌ scheme in which all​​ the gates needed for​​​‌ universal quantum computation could​ be applied on non-overlapping​‌ subspaces in such a​​ way that all the​​​‌ locally occurring errors were​ correctable. More specifically, the​‌ objective is to find​​ an encoding $ℰ$ mapping​​​‌ the logical space to​ the physical space such​‌ that for any unitary​​ $𝒱$ acting on the​​​‌ logical space, there exist​ unitaries ${𝒱}_1,‌\cdots ,{𝒱}_{\mathrm{n}}$ acting on the physical​​​‌ space such that

This scheme would​ allow for errors in​‌ the implementation of the​​ gates to be corrected​​​‌ before they have propagated​ through the computation and​‌ rendered its results useless.​​ Unfortunately, transversality of all​​​‌ the gates needed for​ universal computation and local​‌ correctability within the blocks​​ cannot both be simultaneously​​​‌ satisfied for finite dimensional​ codes. This was proven​‌ by Eastin and Knill​​ in a landmark paper​​​‌ in 2009 81.​ Subsequently, workarounds have been​‌ found. For example, one​​ of the current frontrunner​​​‌ approaches is to apply​ all but one of​‌ the gates needed for​​ universal computation transversally, while​​​‌ the remaining gate is​ applied in a non-transversal​‌ way using other costly​​ techniques.

We have developed​​​‌ in a series of​ two papers 111,​‌ 113, a new​​ method for quantum error​​​‌ correction which is not​ based on this approach.​‌ In this technique, all​​ of the gates in​​​‌ the set needed for​ universal computation are treated​‌ on an equal footing.​​ More precisely, rather than​​​‌ circumventing the Eastin-Knill theorem​ by having one non-transversal​‌ gate, all gates from​​ the universal set can​​​‌ be applied transversally, and​ local errors corrected, but​‌ at the price of​​ an error in the​​​‌ decoding. As long as​ the error in the​‌ decoding is kept small,​​ it will not disrupt​​​‌ the computation and is​ thus not significant from​‌ a practical point of​​ view. To do so,​​​‌ it uses quantum reference​ frames and randomness to​‌ encode the information about​​ which gate was applied​​​‌ during the computation. As​ the quality of the​‌ reference frame increases, the​​ error in the decoding​​​‌ approaches zero. The concept​ of a quantum reference​‌ frame was introduced in​​ the field of quantum​​​‌ foundations in the context​ of sharing so-called “unspeakable​‌ information”, such as the​​ relative orientation of two​​​‌ distant observes. While it​ has been used over​‌ the years in various​​ problems in quantum information​​​‌ theory, its use in​ quantum error correction has​‌ yet to be fully​​ explored.

While this work​​​‌ on the circumvention of​ the Eastin-Knill theorem has​‌ attracted a lot of​​ attention and follow up​​ work by other research​​​‌ groups (see e.g. Refs.‌ 97, 114,‌​‌ 106 and 96),​​ it is not yet​​​‌ ready for primetime. The‌ reason for this, it‌​‌ that while the encoded​​ states are readily fault​​​‌ tolerant (due to the‌ transversality of its gates),‌​‌ the current protocol for​​ applying the encoding and​​​‌ decoding channels are not‌ fault tolerant. This is‌​‌ down to the method​​ in which the quantum​​​‌ reference frames are constructed.‌ However, we believe that‌​‌ finding protocols for implementing​​ the encoder and decoder​​​‌ in a fault tolerant‌ way is a surmountable‌​‌ challenge. We plan to​​ use a recent construction​​​‌ of unitary $t$-designs‌ that use a constant‌​‌ number of non-Clifford gates.​​ Implementing the Clifford gates​​​‌ in the circuit can‌ be done in a‌​‌ transversal way and for​​ the non-Clifford gates, a​​​‌ constant number of magic‌ states can be used.‌​‌ This is analogous in​​ some ways to the​​​‌ entanglement needed to perform‌ magic state distillation 67‌​‌, which is the​​ building block of one​​​‌ of the leading proposals‌ for fault tolerant quantum‌​‌ computation. However, there are​​ many potential benefits to​​​‌ the proposed use of‌ the initial entanglement resource‌​‌ over that of the​​ magic state distillation approach​​​‌ — it is these‌ benefits, which are the‌​‌ key to why this​​ approach could become the​​​‌ chosen method to implement‌ error correction. This includes‌​‌ the fact that the​​ amount of entanglement needed​​​‌ is independent of the‌ computation as well as‌​‌ the high adaptability of​​ this method.

3.3.1​​​‌ Quantum control in quantum​ information processing

One of​‌ the intrinsic limitations of​​ the standard quantum circuit​​​‌ model is that the​ structure of the circuit,​‌ and hence of the​​ flow of information, is​​​‌ fixed prior to computation;​ quantum circuits do not​‌ allow for the possibility​​ of a “quantum if​​​‌-statement”. In this research​ goal we study new​‌ models to quantum computation​​ that, in contrast, have​​​‌ explicit quantum control structures​. These models, in​‌ particular, have the potential​​ to provide new approaches​​​‌ to mitigate noise and​ can lead to stronger​‌ quantum advantages in certain​​ applications.

To study quantum​​​‌ control structures we work​ within the framework of​‌ higher-order quantum operations 71​​, 99, which​​​‌ formalise the types of​ ways quantum circuits or​‌ channels can themselves be​​ transformed within quantum theory.​​​‌ This approach has developed​ rapidly in recent years​‌ 107 since it was​​ first used to show​​​‌ that one can indeed​ formulate quantum computations in​‌ which the order of​​ two quantum gates is​​​‌ superposed with the help​ of a quantum control​‌ system, a gadget known​​ as the quantum switch​​​‌ 72 (see Fig. 3​).

By allowing the​‌ structure of a circuit​​ to be controlled by​​​‌ a quantum system, one​ can perform certain computations​‌ more efficiently. Such “quantum​​ control structures” can be​​​‌ formally studied as higher-order​ quantum operations, leading to​‌ a generalisation of quantum​​ circuits.

The quantum switch and​​ related computations have since​​​‌ been shown to provide​ new types of quantum​‌ advantages in several information-theoretical​​ tasks 74, 59​​​‌, 89, where​ they outperform even “standard”​‌ quantum circuits. Moreover, its​​ relevance for improving noise​​​‌ tolerance has recently come​ to light in a​‌ number of works showing​​ how quantum control can​​​‌ be used to improve​ communication over noisy quantum​‌ channels 82, 73​​,58.

This​​​‌ progress emphasises the potential​ benefits in studying such​‌ models of quantum information​​ processing, and motivates a​​​‌ more systematic study of​ quantum control models in​‌ this context. In a​​ first step in this​​​‌ direction we recently formalised​ a computational model strictly​‌ generalising quantum circuits, called​​ quantum circuits with quantum​​​‌ control of causal order​ (QC-QC) that incorporate –​‌ and generalise – quantum​​ control structures 108.​​​‌ This model will serve​ as the base for​‌ a systematic study of​​ the computational power of​​ quantum computations exploiting quantum​​​‌ control, allowing us‌ to understand the types‌​‌ of advantages this new​​ resource of quantum control​​​‌ can provide.

With a‌ better understanding of quantum‌​‌ computations with quantumly controlled​​ operations, we will aim​​​‌ to develop algorithms for‌ several problems where quantum‌​‌ control appears to be​​ a promising problem. Of​​​‌ particular interest, we will‌ look to use it‌​‌ to provide new algorithms​​ for quantum metrology and​​​‌ parameter estimation – both‌ key problems that are‌​‌ seen as near-to-mid-term applications​​ for quantum information –​​​‌ that are more efficient‌ than existing approaches and,‌​‌ in particular, are more​​ robust in the noisy​​​‌ versions of these problems.‌ An important first step‌​‌ we are undertaking in​​ this direction is to​​​‌ generalise existing advantages obtainable‌ with quantum circuits with‌​‌ quantum control of causal​​ order from problems in​​​‌ a noiseless regime –‌ where the controlled operations‌​‌ are unitary – to​​ a noisy regime, where​​​‌ the controlled operations are‌ noisy quantum channels.

In‌​‌ order to obtain such​​ results, the mathematical tools​​​‌ being studied and developed‌ in the other research‌​‌ axes of the proposed​​ team, most notably convex​​​‌ optimisation, will be of‌ utmost importance (e.g., Goals‌​‌ 3.1.3, 3.1.4 and​​ 3.2.1). These research​​​‌ goals also build on‌ existing collaborations on quantum‌​‌ control of causal order​​ with physicists at the​​​‌ Institut Néel in Grenoble‌ (including on the development‌​‌ of QC-QCs 108),​​ in order to transfer​​​‌ physical insight on quantum‌ control towards new application‌​‌ for information processing. We​​ likewise plan to collaborate​​​‌ with the CAPP team‌ at LIG to study‌​‌ diagrammatic calculi to understand​​ how these new types​​​‌ of computations can be‌ composed and compiled, building‌​‌ on existing collaborations with​​ Mehdi Mhalla on quantum​​​‌ control 58.

The‌ quantum control of quantum‌​‌ operations has potential as​​ a resource throughout quantum​​​‌ information processing: not just‌ for quantum computation but,‌​‌ e.g., also for quantum​​ communication 89. As​​​‌ an example, it can‌ be used to send‌​‌ messages through a quantum​​ network in a superposition​​​‌ of different paths, amounting‌ to a novel extension‌​‌ of quantum Shannon theory​​ 73. By doing​​​‌ so, it has recently‌ been shown in a‌​‌ simple, proof-of-principle setting, that​​ one can notably reduce​​​‌ the effect of noise‌ on the message as‌​‌ it traverses a network​​82, 58 and​​​‌ the effect experimentally verified‌ 101. We will‌​‌ study this possibility further,​​ looking at how it​​​‌ can be extended to‌ practical network topologies and‌​‌ aim to show how​​ it can be exploited​​​‌ to improve quantum communication‌ protocols and lead to‌​‌ novel approaches for quantum​​ cryptography.

One can also​​​‌ generalize the model of‌ computation one step further.‌​‌ In causally indefinite models​​ of computations such as​​​‌ QC-QCs the relative order‌ between gates is rendered‌​‌ indefinite through the use​​ of quantum control systems.​​​‌ Nonetheless, the computation itself‌ still proceeds in the‌​‌ presence of a fixed,​​ causal clock or external​​​‌ control. We will seek‌ to go one step‌​‌ further in the quantum-classical​​​‌ divide and allow for​ this external control to​‌ also be quantum and​​ autonomous. This would require​​​‌ the addition of another​ quantum system implementing the​‌ quantum gates themselves. In​​ the case of a​​​‌ fixed causal order, this​ autonomous device needs its​‌ own internal notion of​​ time, hence it should​​​‌ also be an accurate​ quantum clock 112.​‌ Since it is quantum,​​ this clock which controls​​​‌ the interactions can be​ prepared in a superposition​‌ of different time states,​​ leading to new types​​​‌ of non-casually implemented gates​ and potentially novel applications.​‌

3.3.2 Multipartite entanglement and​​ its applications

Multipartite entanglement​​​‌ plays an important role​ in quantum protocols and​‌ in quantum games, and​​ is likewise a key​​​‌ resource for measurement-based quantum​ computing. Nonetheless, our understanding​‌ of multipartite entanglement as​​ a resource is much​​​‌ less developed than for​ the simpler, but important,​‌ case of bipartite entanglement.​​ The objective of this​​​‌ task is develop our​ understanding of multipartite entanglement,​‌ how it can contribute​​ to reducing the effect​​​‌ of noise in communication,​ computation and more generally​‌ how it can improve​​ coordination in multipartite scenarios.​​​‌

In particular, we plan​ consider communication problems over​‌ noisy classical networks and​​ quantify the extent to​​​‌ which multipartite nonlocality can​ improve the transmission rates​‌ 98. Focussing on​​ relevant classical network communication​​​‌ scenarios, we will ask​ whether entanglement between some​‌ of the involved parties​​ significantly improve the rates.​​​‌

In a related direction,​ we plan to study​‌ game-theoretic settings with players​​ with divergent interests and​​​‌ the advantage that can​ be achieved by using​‌ multipartite entangled states and,​​ in particular, quantum graph​​​‌ states 88. In​ collaboration with Mehdi Mhalla,​‌ we will aim to​​ use such advantages to​​​‌ provide new approaches to​ certify multipartite entangled states,​‌ and in particular to​​ self-test quantum graph states​​​‌ – important resources in​ certain quantum computational models​‌ – by certifying them​​ solely from the correlations​​​‌ they produce 62,​ 61. We plan​‌ to use progress towards​​ Goal 3.1.4 to provide​​​‌ a finer analysis of​ the problem.

3.3.3 Quantum​‌ frequential computing

This is​​ a new research direction​​​‌ of the team, which​ focuses on developing a​‌ new type of quantum​​ computer that achieves speed-ups​​​‌ in both quantum and​ classical computation. In a​‌ nutshell, it will focus​​ on showing that when​​​‌ the bit/qubit control is​ quantum, then a large​‌ quadratic speedup, as a​​ fuction of the underlying​​​‌ resources, is achievable. This​ constitutes a new type​‌ of quantum resource since​​ traditioanlly the bit/qubit control​​​‌ is considered to be​ classical or semi-calssical.

We​‌ are developing two intertwined​​ directions of research with​​​‌ this objective in mind:​

5.1.1 BellPolytopes.jl​​​‌

• Keywords:
  Mathematical Optimization, Quantum‌ Information
• Functional Description:
  BellPolytopes.jl‌​‌ aims at constructing Bell​​ inequalities and local models​​​‌ via Frank-Wolfe algorithms.
• Contact:‌
  Sebastien Designolle
• Partner:
  Zuse‌​‌ Institute Berlin

5.1.2 EntanglementDetection.jl​​

• Keywords:
  Quantum Information, Mathematical​​​‌ Optimization
• Functional Description:
  Separability‌ decomposition and entanglement detection‌​‌ via Frank-Wolfe algorithms.
• Contact:​​
  Sebastien Designolle
• Partner:
  Zuse​​​‌ Institute Berlin

5.1.3 Ket.jl‌

• Name:
  Ket.jl: Toolbox for‌​‌ quantum information, nonlocality and​​ entanglement
• Keywords:
  Julia programming​​​‌ language, Quantum Information
• Functional‌ Description:
  Ket.jl is a‌​‌ toolbox for quantum information,​​ nonlocality and entanglement written​​​‌ in the Julia programming‌ language.
• URL:
  https://­dev-ket.­github.­io/­Ket.­jl/­dev/
• Contact:‌​‌
  Sebastien Designolle
• Partners:
  Universidad​​ de Valladolid, University of​​​‌ Siegen, LIP6, Zuse Institute‌ Berlin

5.1.4 FrankWolfe.jl

• Keyword:‌​‌
  Mathematical Optimization
• Functional Description:​​
  FrankWolfe.jl is a toolbox​​​‌ for Frank-Wolfe and conditional‌ gradients algorithms.
• URL:
  https://­zib-iol.­github.­io/­FrankWolfe.­jl/­dev/‌​‌
• Contact:
  Mathieu Besancon
• Partner:​​
  Zuse Institute Berlin

Efficient estimation of properties​​​‌ of quantum devices

Estimating​ the fidelity between a​‌ desired target quantum state​​ and an actual prepared​​​‌ state is essential for​ assessing the success of​‌ experiments. In 16,​​ for pure target states,​​​‌ we use functional representations​ that can be measured​‌ directly and determine the​​ number of copies of​​​‌ the prepared state needed​ for fidelity estimation. In​‌ continuous variable (CV) systems,​​ we use the Wigner​​​‌ function, which can be​ measured via displaced parity​‌ measurements. We provide upper​​ and lower bounds on​​​‌ the sample complexity required​ for fidelity estimation, considering​‌ the worst-case scenario across​​ all possible prepared states.​​​‌ For target states of​ particular interest, such as​‌ Fock and Gaussian states,​​ we find that this​​​‌ sample complexity is characterized​ by the $L_{\mathrm{1‌}}$-norm of the Wigner​​ function, a measure of​​​‌ Wigner negativity widely studied​ in the literature, in​‌ particular in resource theories​​ of quantum computation.

In​​​‌ another work 15,​ we consider the problem​‌ of estimating the noise​​ of a quantum device.​​​‌ We show that in​ many settings, the state-of-the-art​‌ method for learning the​​ parameters of a Pauli​​​‌ channel is optimal in​ terms of the number​‌ of queries.

Simulation of​​ noisy quantum circuits

As​​​‌ quantum devices continue to​ grow in size but​‌ remain affected by noise,​​ it is crucial to​​​‌ determine when and how​ they can outperform classical​‌ computers on practical tasks.​​ A central piece in​​​‌ this effort is to​ develop the most efficient​‌ classical simulation algorithms possible.​​ Among the most promising​​​‌ approaches are Pauli backpropagation​ algorithms, which have already​‌ demonstrated their ability to​​ efficiently simulate certain classes​​​‌ of parameterized quantum circuits-a​ leading contender for near-term​‌ quantum advantage-under random circuit​​ assumptions and depolarizing noise.​​​‌ However, their efficiency was​ not previously established for​‌ more realistic non-unital noise​​ models, such as amplitude​​​‌ damping, that better capture​ noise on existing hardware.​‌ In 17, we​​ close this gap by​​​‌ adapting Pauli backpropagation to​ non-unital noise, proving that​‌ it remains efficient even​​ under these more challenging​​​‌ conditions. Our proof leverages​ a refined combinatorial analysis​‌ to handle the complexities​​ introduced by non-unital channels,​​​‌ thus strengthening Pauli backpropagation​ as a powerful tool​‌ for simulating near-term quantum​​ devices.

Security of differential​​​‌ phase shift quantum key​ distribution

The design of​‌ quantum protocols for secure​​ key generation poses many​​​‌ challenges: On the one​ hand, they need to​‌ be practical concerning experimental​​ realisations. On the other​​​‌ hand, their theoretical description​ must be simple enough​‌ to allow for a​​ security proof against all​​​‌ possible attacks. Often, these​ two requirements are in​‌ conflict with each other,​​ and the differential phase​​​‌ shift (DPS) QKD protocol​ exemplifies these difficulties: It​‌ is designed to be​​ implementable with current optical​​​‌ telecommunication technology, which, for​ this protocol, comes at​‌ the cost that many​​ standard security proof techniques​​​‌ do not apply to​ it. After about 20​‌ years since its invention,​​ 20 presents the first​​​‌ full security proof of​ DPS QKD against general​‌ attacks, including finite-size effects.​​ The proof combines techniques​​ from quantum information theory,​​​‌ quantum optics, and relativity.‌ We first give a‌​‌ security proof of a​​ QKD protocol whose security​​​‌ stems from relativistic constraints.‌ We then show that‌​‌ security of DPS QKD​​ can be reduced to​​​‌ security of the relativistic‌ protocol. In addition, we‌​‌ show that coherent attacks​​ on the DPS protocol​​​‌ are, in fact, stronger‌ than collective attacks. Our‌​‌ results have broad implications​​ for the development of​​​‌ secure and reliable quantum‌ communication technologies, as they‌​‌ shed light on the​​ range of applicability of​​​‌ stateof-the-art security proof techniques.‌

Fault-tolerant‌ quantum input/output

Usual scenarios‌​‌ of fault-tolerant computation are​​ concerned with the fault-tolerant​​​‌ realization of quantum algorithms‌ that compute classical functions,‌​‌ such as Shor's algorithm​​ for factoring. In particular,​​​‌ this means that input‌ and output to the‌​‌ quantum algorithm are classical.​​ In contrast to stand-alone​​​‌ single-core quantum computers, in‌ many distributed scenarios, quantum‌​‌ information might have to​​ be passed on from​​​‌ one quantum information processing‌ system to another one,‌​‌ possibly via noisy quantum​​ communication channels with noise​​​‌ levels above fault-tolerant thresholds.‌ In such situations, quantum‌​‌ information processing devices will​​ have quantum inputs, quantum​​​‌ outputs or even both,‌ which pass qubits among‌​‌ each other. Working in​​ the fault-tolerant framework of​​​‌ 94, we show‌ in 28 that any‌​‌ quantum circuit with quantum​​ input and output can​​​‌ be transformed into a‌ fault-tolerant circuit that produces‌​‌ the ideal circuit with​​ some controlled noise applied​​​‌ at the input and‌ output. The framework allows‌​‌ the direct composition of​​ the statements, enabling versatile​​​‌ future applications. We illustrate‌ this with two concrete‌​‌ applications. The first one​​ concerns communication over a​​​‌ noisy channel with faulty‌ encoding and decoding operations‌​‌ 75. For communication​​ codes with linear minimum​​​‌ distance, we construct fault-tolerant‌ encoders and decoders for‌​‌ general noise (including coherent​​ errors). For the weaker,​​​‌ but standard, model of‌ local stochastic noise, we‌​‌ obtain fault-tolerant encoders and​​ decoders for any communication​​​‌ code that can correct‌ a constant fraction random‌​‌ errors. In the second​​ application presented 11,​​​‌ we use our result‌ for a state preparation‌​‌ circuit within the construction​​ of 87 to establish​​​‌ that fault-tolerant quantum computation‌ for general noise can‌​‌ be achieved with constant​​ space overhead.

Monogamy of entanglement between​​​‌ cones

Monogamy is one‌ of the important features‌​‌ of quantum entanglement that​​ underlies many of its​​​‌ information-theoretic applications. In 6‌, We show that‌​‌ monogamy is not only​​ a feature of quantum​​​‌ theory, but that it‌ characterizes the minimal tensor‌​‌ product of general pairs​​ of convex cones ${\mathrm{C‌}}_A$ and $C_{\mathrm{B‌}}$: The elements of‌​‌ the minimal tensor product​​ $C_A{\otimes }_{min‌}{C}_B$ are precisely‌ the tensors that can‌​‌ be symmetrically extended to​​ elements in the maximal​​​‌ tensor product $C_{\mathrm{A‌}}{\otimes }_{max}{C}_{\mathrm{B‌‌}}^{{\otimes }_{max}k}$ for​​​‌ every $k\in \mathrm{\mathbb{N}}$.

First-order optimisation methods​‌ for quantum information

In​​ 8, 50,​​​‌ we develop and apply​ scalable first-order optimisation techniques​‌ based on Frank–Wolfe algorithms​​ to problems in quantum​​​‌ information. In 8,​ we introduce major improvements​‌ to the open-source Julia​​ package FrankWolfe.jl, extending​​​‌ its capabilities, efficiency, and​ usability for large-scale convex​‌ optimisation. These developments are​​ directly exploited in 50​​​‌, where Frank-Wolfe methods​ are applied to entanglement​‌ detection problems, enabling the​​ treatment of instances that​​​‌ are out of reach​ for standard semidefinite programming​‌ approaches. This work also​​ led to the development​​​‌ of a dedicated open-source​ library, EntanglementDetection.jl, facilitating​‌ the practical use of​​ these methods in quantum​​​‌ information research.

Communication-assisted classical​ models of Bell nonlocality​‌

The work 54 investigates​​ Bell nonlocality from an​​​‌ operational perspective by studying​ classical models augmented with​‌ limited communication. Specifically, we​​ consider scenarios in which​​​‌ Alice is allowed to​ communicate her measurement outcome​‌ to Bob, and analyse​​ which forms of nonclassical​​​‌ correlations can then be​ reproduced. This approach provides​‌ insight into the minimal​​ physical ingredients that must​​​‌ be added to classical​ physics in order to​‌ recover quantum correlations, and​​ helps clarify the role​​​‌ of communication as a​ resource in Bell-type scenarios.​‌

Measurement incompatibility and EPR​​ steering

The articles 34​​​‌, 39 address the​ problem of characterising and​‌ quantifying measurement incompatibility, a​​ key nonclassical feature underlying​​​‌ EPR steering. In 34​, we develop analytical​‌ tools to derive universal​​ bounds on measurement incompatibility​​​‌ and identify extremal measurement​ configurations. Complementarily, 39 focuses​‌ mostly on qubit systems​​ and introduces numerical methods​​​‌ to explore incompatibility and​ steering in concrete scenarios.​‌ Together, these works provide​​ a unified analytical and​​​‌ numerical perspective on the​ structure of incompatible measurements​‌ and their role as​​ a resource in quantum​​​‌ information tasks.

Bridging indefinite causality and​ composable quantum protocols in​‌ space-time

The concept of​​ quantum processes with indefinite​​​‌ causal orders (ICO) have​ garnered much interest due​‌ to their potential advantages​​ for information processing. However,​​​‌ there have remained longstanding​ open questions regarding the​‌ physical realisability of ICO​​ processes. Moreover, it was​​​‌ previously observed that composition​ of such processes is​‌ not so straightforward, which​​ raises the question of​​​‌ how this connects with​ the observed composability of​‌ physical experiments. In 19​​, we address these​​​‌ questions by bridging these​ information-theoretic approaches for causality,​‌ with spacetime structure which​​ constraints physical implementations. Specifically,​​​‌ we connect the formalism​ of quantum circuits with​‌ quantum control of causal​​ order (QC-QC), which models​​​‌ an important class of​ ICO processes, with that​‌ of causal boxes, which​​ models composable quantum information​​​‌ protocols in spacetime. We​ incorporate the set-up assumptions​‌ of the QC-QC framework​​ into the spatiotemporal perspective​​​‌ and show that every​ QC-QC can be mapped​‌ to a causal box​​ that satisfies these set​​​‌ up assumptions and acts​ on a Fock space​‌ while reproducing the QC-QC's​​ behaviour in a relevant​​ subspace. We show that​​​‌ the causal box corresponds‌ to a fine-grained description‌​‌ of the QC-QC, which​​ unravels the original ICO​​​‌ of the QC-QC into‌ a set of quantum‌​‌ operations with a well-defined​​ and acyclic causal order,​​​‌ compatible with the spacetime's‌ light cone structure. Through‌​‌ this mapping, we clarify​​ how the composability of​​​‌ physical experiments is recovered,‌ and the role of‌​‌ relativistic causality.

Query complexity​​ of causally indefinite classical​​​‌ and quantum computation

Indefinite‌ causal order opens interesting‌​‌ possibilities for information processing,​​ such as the possibility​​​‌ to obtain computational advantages‌ using causally indefinite computations‌​‌ beyond what is possible​​ with standards (causally ordered)​​​‌ circuits. In the recent‌ work 57 we studied‌​‌ the computational advantages of​​ quantum causal indefiniteness in​​​‌ query complexity problems using‌ the framework of quantum‌​‌ supermaps, showing that advantages​​ can be obtained for​​​‌ certain types of functions,‌ uncovering a new computational‌​‌ advantage of causal indefiniteness​​ that, in contrast to​​​‌ previously known advantages, is‌ formulated in a more‌​‌ standard complexity-theoretic setting. In​​ a follow up work​​​‌ 24, we study‌ the query complexity of‌​‌ causally indefinite “classical” computations.​​ In this simpler, but​​​‌ previously unstudied setting, allowing‌ us to obtain –‌​‌ in contrast to what​​ has been proven in​​​‌ the quantum setting –‌ asymptotic advantages in query‌​‌ complexity. We study whether​​ these advantages can be​​​‌ transformed into quantum ones,‌ obtaining new quantum advantages‌​‌ in the exact (rather​​ than bounded-error) setting, and​​​‌ highlight roadblocks to transforming‌ them into asymptotic quantum‌​‌ advantages.

Dynamical causal structures​​

While we typically think​​​‌ of classical causal structures‌ as being fixed (or,‌​‌ at best, probabilistically fixed),​​ it has been understood​​​‌ for some time that‌ more subtle possibilities exist:‌​‌ the causal structure between​​ future events can depend​​​‌ on those in the‌ past, a possibility known‌​‌ as dynamical causal structure.​​ Indefinite causal structures thus​​​‌ must not be dynamically‌ fixed, and much recent‌​‌ work has studied how​​ quantum effects such as​​​‌ superposition can lead to‌ causally indefinite processes. In‌​‌ such quantum settings, however,​​ it becomes difficult to​​​‌ disentangle dynamical from quantum‌ causal structures; for example,‌​‌ are some causally indefinite​​ quantum structures dynamical, while​​​‌ others are not? Until‌ now, the notion of‌​‌ dynamicality had not been​​ studied in its own​​​‌ right, and the formalism‌ to study such questions‌​‌ was lacking. In 51​​ we provide a first​​​‌ rigorous study of the‌ concept, both for causal‌​‌ correlations and quantum processes,​​ within the QC-QC framework.​​​‌ We uncover a new,‌ subtly way that causal‌​‌ order can be dynamical​​ without being explicitly influenceable​​​‌ be parties acting in‌ the past. We characterise‌​‌ the classes of correlations​​ and processes with non-dynamical​​​‌ causal order, allowing us‌ to formalise precisely in‌​‌ which sense certain quantum​​ processes can have both​​​‌ indefinite and dynamical causal‌ order.

Internal “routed” structure‌​‌ of coherently controlled circuits​​

In recent years, several​​​‌ diffierent frameworks have emerged‌ to study quantum computations‌​‌ or, more generally, processes​​ with indefinite causal order.​​​‌ Amongst these, quantum circuits‌ with quantum control of‌​‌ causal order (QC-QCs) has​​​‌ emerged as a particularly​ relevant framework describing a​‌ broad class of higher-order​​ quantum operations with physical​​​‌ interpretations in a generalised​ circuit framework. The framework​‌ of routed quantum circuitss​​ (RQCs), on the other​​​‌ hand, allows the fine-grained​ internal causal structure of​‌ quantum operations to be​​ studied in a compositional​​​‌ manner, building from an​ underlying “routed graph”. However,​‌ little is known about​​ the expressivity of the​​​‌ RQC framework. In 46​, we show how​‌ any QC-QC can represented​​ as a RQC in​​​‌ a rather general, constructive​ manner. This thereby links​‌ this two important frameworks,​​ and provides novel new​​​‌ insights into the internal​ causal structure of QC-QCs.​‌ One result of this​​ connection, e.g., is the​​​‌ finding that, from $\mathrm{N}=4$ onwards, internal​‌ nodes are generally necessary​​ to represent QC-QCs as​​​‌ RQCs, an observation that​ constrains any physical realisiation​‌ of such computations.

Cyclic​​ causal models with a​​​‌ graph separation theorem

Causal​ models are essential for​‌ formally linking correlations to​​ causal explanations. A majority​​​‌ of established results focus​ on acyclic causal structures.​‌ Cyclic causal models are​​ crucial for describing feedback​​​‌ in physical systems and​ exotic fundamental scenarios, but​‌ pose major challenges: they​​ lack a general probability​​​‌ rule, and the $\mathrm{d}$-separation theorem (central to​‌ causal reasoning in the​​ acyclic case) fails even​​​‌ in classical cyclic models.​ In 43, 42​‌, comprehensive frameworks were​​ introduced for all consistent​​​‌ classical and quantum cyclic​ causal models on finite-dimensional​‌ systems, which address this​​ gap by providing a​​​‌ robust probability rule and​ the first sound and​‌ complete graph-separation property, $\mathrm{p}$-separation applicable to these​​​‌ general cyclic models. The​ approach maps cyclic models​‌ to acyclic ones with​​ post-selection, the frameworks are​​​‌ developed separately for the​ quantum information and classical​‌ statistics communities in 43​​ and 42, and​​​‌ proven to be mutually​ compatible. The concept of​‌ a generalised post-selected teleportation​​ protocol is introduced both​​​‌ for quantum states and​ classical probabilities to achieve​‌ this. The work generalises​​ several existing causality formalisms​​​‌ and provides a rigorous​ foundation for cyclic quantum​‌ and classical causal discovery.​​

Wigner's Friend scenarios, contextuality​​​‌ and the measurement problem​

Wigner's Friend scenarios explore​‌ the foundational consequences of​​ modeling reasoning agents as​​​‌ physical quantum systems, and​ their study shares deep​‌ connections with the (infamous)​​ quantum measurement problem. The​​​‌ works 52 and 18​ propose frameworks to extending​‌ these studies beyond quantum​​ theory. In 52,​​​‌ a link between Wigner's​ Friend type multi-agent paradoxes​‌ and contextuality is proven​​ in general theories: if​​​‌ agents who are modeled​ within a physical theory​‌ come to a contradiction​​ when reasoning using that​​​‌ theory (under certain assumptions​ on how they reason​‌ and describe measurements), then​​ the theory must admit​​​‌ contextual correlations of a​ logical form. The work​‌ further characterises properties of​​ such paradoxes in general​​​‌ theories vs quantum theory,​ owing to the structure​‌ of quantum contextual correlations.​​ In 18, it​​​‌ is shown that any​ theory that satisfies the​‌ properties of Bell Nonlocality,​​ Information Preservation, and Local​​ Dynamics, has a measurement​​​‌ problem, in the sense‌ that it makes predictions‌​‌ that are incompatible with​​ measurement outcomes being absolute​​​‌ (that is, unique and‌ non-relational). This highlights that‌​‌ the measurement problem is​​ not specific to quantum​​​‌ theory, while shedding light‌ on what would be‌​‌ required of a future​​ theory of physics to​​​‌ overcome the measurement problem.‌

Equivalence between time symmetry‌​‌ and cyclic causality

The​​ standard operational formulation of​​​‌ quantum theory imposes a‌ definite, acyclic causal order‌​‌ on agents' operations, contrasting​​ with time-symmetric dynamics. Two​​​‌ prominent extensions of this‌ framework are the multi-time‌​‌ state (MTS) formalism, which​​ incorporates time symmetry via​​​‌ arbitrary pre- and post-selection,‌ and the post-selected closed‌​‌ timelike curve (P-CTC) framework,​​ which enables cyclic causal​​​‌ influences through post-selection on‌ maximally entangled states. While‌​‌ prior work has noted​​ structural connections between MTS​​​‌ and P-CTCs, it remained‌ unclear whether there is‌​‌ an operational equivalence between​​ the most general objects​​​‌ of the two formalisms.‌ 48, addresses this‌​‌ gap by extending the​​ P-CTC framework to define​​​‌ time-labelled P-CTC assisted combs,‌ a more general class‌​‌ of P-CTC-assisted objects that​​ support open processing slots​​​‌ and explicit temporal structure.‌ It is proven, via‌​‌ explicit constructions, that for​​ every (possibly mixed) MTS,​​​‌ there exists an operationally‌ equivalent time-labelled P-CTC-assisted comb,‌​‌ and vice versa. A​​ resource-theoretic view of MTS​​​‌ is also explored, by‌ defining a partial order‌​‌ under free transformations that​​ do not use P-CTCs.​​​‌

Operational approach for events‌ and their localisation without‌​‌ background spacetime

The notions​​ of events and their​​​‌ localisation fundamentally differ between‌ quantum theory and general‌​‌ relativity, reconciling them becomes​​ even more important and​​​‌ challenging in the context‌ of quantum gravity where‌​‌ a classical spacetime background​​ can no longer be​​​‌ assumed. 55 therefore proposes‌ an operational approach drawing‌​‌ from quantum information, to​​ define events and their​​​‌ localisation relative to a‌ structure called a Lab,‌​‌ which in particular includes​​ a choice of physical​​​‌ degree of freedom (the‌ reference) providing a generalised‌​‌ notion of "location". The​​ work defines a property​​​‌ of the reference, relative‌ measurability, that is sensitive‌​‌ to correlations between the​​ Lab's reference and objects​​​‌ of study. Applying this‌ proposal to analyse the‌​‌ quantum switch (QS), a​​ process widely associated with​​​‌ indefinite causal order, the‌ work uncovers differences between‌​‌ classical and quantum spacetime​​ realisations of QS, rooted​​​‌ in the relative measurability‌ of the associated references.‌​‌ The analysis clarifies a​​ longstanding debate on the​​​‌ interpretation of QS experiments,‌ demonstrating how different conclusions‌​‌ stem from distinct assumptions​​ on the Labs and​​​‌ agents' allowed interventions. This‌ provides a foundation for‌​‌ a more unified view​​ of events, localisation, and​​​‌ causality across quantum and‌ relativistic domains.

7.1.1 Horizon Europe​​​‌

7.1.2 H2020 projects

7.1.3 Other​‌ european programs/initiatives

PEPR DIQKD

• Title:​
  Device-independent quantum key distribution​‌
• Program:
  PEPR on Quantum​​ Technologies
• Contact Inria:
  O.​​​‌ Fawzi
• Partners:
  CEA (coordinator),​ CNRS, Université Côte D’Azur,​‌ Sorbonne Université
• Duration:
  July​​ 1, 2022 - June​​​‌ 30 2026

PEPR NISQ2LSQ​

• Title:
  From NISQ to​‌ LSQ: Bosonic and LDPC​​ codes
• Program:
  PEPR on​​​‌ Quantum Technologies
• Contact Inria:​
  A. Leverrier (team COSMIQ)​‌
• Contact QInfo:
  O. Fawzi​​
• Partners:
  Inria (coordinator), CNRS,​​​‌ CEA
• Duration:
  January 1,​ 2022 - December 2026​‌

PEPR EPIQ

• Title:
  Study​​ of the quantum stack:​​​‌ Algorithm, models, and simulation​ for quantum computing
• Program:​‌
  PEPR on Quantum Technologies​​
• Contact Inria:
  S. Perdrix​​​‌ (team MOCQUA)
• Contact QInfo:​
  O. Fawzi
• Partners:
  Inria​‌ (coordinator), CNRS, CEA
• Duration:​​
  January 1, 2022 -​​​‌ December 2026

ANR TaQC​

• Title:
  Taming Quantum Causality​‌
• Program:
  AAP Générique 2022​​
• Contact QInfo:
  A. Abbott​​​‌
• Partners:
  CNRS (Institut Néel;​ coordinator), Inria QINFO, Université​‌ Paris-Saclay (LMF, Inria QUACS),​​ CEA (IRFU/LARSIM)
• Duration:
  January​​​‌ 1, 2023 - December​ 2026

8.1.1 Scientific​​​‌ events: organisation

8.1.2 Scientific​​​‌ events: selection

8.1.3‌ Journal

8.1.4 Invited talks

• O.​​​‌ Fawzi, TENORS Network Learning‌ Week, Sophia-Antipolis, February 2025‌​‌
• O. Fawzi, Quantum Certification​​ Conference+, Warsaw, May 2025​​​‌
• O. Fawzi, Mathematics of‌ Quantum Information Workshop, Aachen,‌​‌ July 2025
• O. Fawzi,​​ Enhanced Quantum Information Workshop,​​​‌ Munich, October 2025
• M.‌ Woods, Seminar at IBM‌​‌ Zurich, February 2025
• M.​​ Woods, Seminar at Johannes​​​‌ Kepler University, Austria, November‌ 2025
• V. Vilasini, Quantum‌​‌ Information Structure of Spacetime​​ (QISS) conference, Vienna, April​​​‌ 2025
• V. Vilasini, New‌ Directions in the Foundations‌​‌ of Physics, Slovenia, May​​ 2025
• V. Vilasini, GdR​​​‌ TeQ colloquium, Grenoble, November‌ 2025
• S. Rao, SIAM‌​‌ Conference on Applied Algebraic​​ Geometry, July 2025
• R.​​​‌ Salzmann, Seminar at Scuola‌ Normale Superiore Pisa, May‌​‌ 2025
• R. Salzmann, Seminar​​ at Institute for Quantum​​​‌ Information RWTH Aachen, September‌ 2025

8.1.5 Leadership within‌​‌ the scientific community

• V.​​ Vilasini is a co-leader​​​‌ of a research working‌ group in the European‌​‌ COST Action for Relativistic​​ Quantum Information

8.1.6 Scientific​​​‌ expertise

• A. Abbott: Member‌ of the selection committee‌​‌ for Inria CRCN and​​ ISFP recrutement competitions, Inria​​​‌ Saclay Centre

8.1.7 Research‌ administration

• A. Abbott is‌​‌ a member of the​​ governing board of the​​​‌ QuantAlps Research Federation
• A.‌ Abbott was a member‌​‌ of the governing board​​ of the TIQuA CD​​​‌ Tools Programme (2022–2025)
• A.‌ Abbott is a member‌​‌ of the direction of​​ the Maison de Quantique​​​‌ Alpes
• O. Fawzi is‌ a member of the‌​‌ steering committee of the​​ GDR TeQ
• O. Fawzi​​​‌ is a member of‌ the external board of‌​‌ QuanTech@Paris

8.2.1 Supervision

• PhD in‌​‌ progress: Maarten Grothus (A.​​ Abbott with C. Branciard).​​​‌
• PhD in progress: Raphaël‌ le Bihan (A. Abbott‌​‌ with M. Echenim).
• PhD​​ in progress: Emilien de​​​‌ Bank (V. Vilasini with‌ C. Branciard).
• PhD in‌​‌ progress: Amanda Maria Fonseca​​ (V. Vilasini with C.​​​‌ Branciard).
• PhD in progress:‌ Pablo Alvarez Dominguez (M.‌​‌ Woods).
• PhD in progress:​​ Emily Beatty (G. Aubrun,​​​‌ D. Stilck França).
• PhD‌ in progress: Victor Martinez‌​‌ (O. Fawzi, D. Stilck​​ França).
• PhD in progress:​​​‌ Mostafa Taheri (O. Fawzi).‌
• PhD in progress: Idris‌​‌ Delsol (O. Fawzi).
• PhD​​ thesis defended in October​​​‌ 2025: Pierre Pocreau (A.‌ Abbott with M. Mhalla).‌​‌
• PhD thesis defended in​​ February 2025: Victor Gitton,​​​‌ ETH Zürich (co-supervisor: V.‌ Vilasini with supervisor: Renato‌​‌ Renner).
• Master's internship (École​​ Polytechnique): Matthieu Bruant (A.​​​‌ Abbott).
• 1A internship (ENS‌ Paris Saclay): Igor Semezies‌​‌ (A. Abbott).
• Master's internship​​ (Unversité Grenoble Alpes): Amine​​​‌ Sidi Ali Cherif (G.‌ Aubrun).
• Master's internship (ETH‌​‌ Zurich): Restrepo Gaviria Pablo​​​‌ (M. Woods).

8.2.2 Juries​

• PhD: Victor Gitton, Certifying​‌ non-classicality in causal networks​​, ETH Zürich, February​​​‌ 2025. (V. Vilasini, co-examiner)​
• PhD: Marin Costes, Dynamical​‌ computations of discrete space-time​​ structures, Université Paris-Saclay,​​​‌ December 2025 (V. Vilasini,​ jury member)
• PhD: Romain​‌ Piron, Quantum Algorithms for​​ NOMA systems, INSA​​​‌ Lyon, October 2025 (O.​ Fawzi, president)
• HDR: Marc-Olivier​‌ Renou, Quantum Information Theory:​​ Foundations, distributed algorithms and​​​‌ nonlocality in quantum networks​, Institut Polytechnique de​‌ Paris, Avril 2025 (O.​​ Fawzi, examiner)
• HDR: Mehdi​​​‌ Mhalla, Discrete tools for​ understanding quantum information,​‌ Université Grenoble Alpes, Avril​​ 2025 (O. Fawzi, referee)​​​‌

8.2.3 Educational and pedagogical​ outreach

• Quantum Computer Science​‌ lecture at ENS Lyon,​​ 2h weekly during the​​​‌ first semester (S. Designolle)​
• Quantum Optics, M2 course,​‌ UGA, 4h (V. Vilasini)​​
• Fundamental Computer Science, M1​​​‌ MOSIG/M1 INFO, UGA. 33h​ lectures and tutorials (A.​‌ Abbott)
• Probability for computer​​ science at ENS Lyon​​​‌ (1st year), 2h weekly​ in both Spring and​‌ Fall semesters (G. Aubrun)​​

8.3.1​‌ Participation in Live events​​

• Participation at "Fête de​​​‌ la Science" at Université​ Lyon 1 (G. Aubrun)​‌
• Participation at "Opération Quantique"​​ to bring research in​​​‌ quantum physics in schools​ (S. Designolle)

International journals

• 5 article​‌G.Guillaume Aubrun and​​ M.Mathis Cavichioli.​​​‌ A characterization of inner​ product spaces via norming​‌ vectors.Canadian Mathematical​​ BulletinJanuary 2025,​​ 1-5HALDOI
• 6​​​‌ articleG.Guillaume Aubrun‌, A.Alexander Müller-Hermes‌​‌ and M.Martin Plávala​​. Monogamy of entanglement​​​‌ between cones.Mathematische‌ Annalen39112025‌​‌, 1591-1609HALDOI​​back to text
• 7​​​‌ articleS.Simon Becker‌, N.Niklas Galke‌​‌, L.Lauritz van​​ Luijk and R.Robert​​​‌ Salzmann. Convergence Rates‌ for the Trotter Splitting‌​‌ for Unbounded Operators.​​Foundations of Computational Mathematics​​​‌September 2025HALDOI‌
• 8 articleM.Mathieu‌​‌ Besançon, S.Sébastien​​ Designolle, J.Jannis​​​‌ Halbey, D.Deborah‌ Hendrych, D.Dominik‌​‌ Kuzinowicz, S.Sebastian​​ Pokutta, H.Hannah​​​‌ Troppens, D.Daniel‌ Viladrich Herrmannsdoerfer and E.‌​‌Elias Wirth. Improved​​ algorithms and novel applications​​​‌ of the FrankWolfe.jl library‌.ACM Transactions on‌​‌ Mathematical SoftwareSeptember 2025​​, 1-31HALDOI​​​‌back to textback‌ to text
• 9 article‌​‌R.Rutvij Bhavsar,​​ L.Lewis Wooltorton and​​​‌ J.Joonwoo Bae.‌ Composable Framework for Device-Independent‌​‌ State Certification.PRX​​ Quantum64December​​​‌ 2025, 040356HAL‌DOI
• 10 articleQ.‌​‌Qian Chen, B.​​Benoît Collins and O.​​​‌Omar Fawzi. Symmetry‌ reduction for testing $\mathrm{k‌‌}$-block-positivity via extendibility.​​Journal of Physics A:​​​‌ Mathematical and Theoretical58‌48November 2025,‌​‌ 485302HALDOI
• 11​​ articleM.Matthias Christandl​​​‌, O.Omar Fawzi‌ and A.Ashutosh Goswami‌​‌. Fault-Tolerant Quantum Computation​​ with Constant Overhead for​​​‌ General Noise.PRX‌ Quantum64November‌​‌ 2025, 040334HAL​​DOIback to text​​​‌
• 12 articleK.Kun‌ Fang, H.Hamza‌​‌ Fawzi and O.Omar​​ Fawzi. Adversarial Quantum​​​‌ Channel Discrimination.Physical‌ Review Letters13526‌​‌December 2025, 260201​​HALDOI
• 13 article​​​‌H.Hamza Fawzi and‌ O.Omar Fawzi.‌​‌ Convergence of linear programming​​ hierarchies for Gibbs states​​​‌ of spin systems.‌Transactions on Machine Learning‌​‌ Research JournalDecember 2025​​HAL
• 14 articleO.​​​‌Omar Fawzi, L.‌Li Gao and M.‌​‌Mizanur Rahaman. Asymptotic​​ Equipartition Theorems in von​​​‌ Neumann algebras.Annales‌ Henri PoincaréFebruary 2025‌​‌, 1-48HAL
• 15​​ articleO.Omar Fawzi​​​‌, A.Aadil Oufkir‌ and D. S.Daniel‌​‌ Stilck França. Lower​​ Bounds on Learning Pauli​​​‌ Channels With Individual Measurements‌.IEEE Transactions on‌​‌ Information TheoryApril 2025​​, 1-32HALDOI​​​‌back to text
• 16‌ articleO.Omar Fawzi‌​‌, A.Aadil Oufkir​​ and R.Robert Salzmann​​​‌. Optimal Fidelity Estimation‌ from Binary Measurements for‌​‌ Discrete and Continuous Variable​​ Systems.PRX Quantum​​​‌71January 2026‌, 010309HALDOI‌​‌back to text
• 17​​ articleV.Victor Martinez​​​‌, A.Armando Angrisani‌, E.Ekaterina Pankovets‌​‌, O.Omar Fawzi​​ and D.Daniel Stilck​​​‌ França. Efficient Simulation‌ of Parametrized Quantum Circuits‌​‌ under Nonunital Noise through​​ Pauli Backpropagation.Physical​​​‌ Review Letters13425‌2025, 250602HAL‌​‌DOIback to text​​
• 18 article N.Nick​​​‌ Ormrod, V.V‌ Vilasini and J.Jonathan‌​‌ Barrett. Which theories​​​‌ have a measurement problem?​ New Journal of Physics​‌ October 2025 HAL DOI​​ back to text back​​​‌ to text
• 19 article​M.Matthias Salzger and​‌ V.V. Vilasini.​​ Mapping indefinite causal order​​​‌ processes to composable quantum​ protocols in a spacetime​‌.New Journal of​​ Physics27February 2025​​​‌, 1-54HALDOI​back to text
• 20​‌ articleM.Martin Sandfuchs​​, M.Marcus Haberland​​​‌, V.V Vilasini​ and R.Ramona Wolf​‌. Security of differential​​ phase shift QKD from​​​‌ relativistic principles.Quantum​9January 2025,​‌ 1611HALDOIback​​ to text
• 21 article​​​‌V.V. Vilasini and​ R.Roger Colbeck.​‌ Theories with no superluminal​​ signaling have greater information-processing​​​‌ power than theories with​ no superluminal causation.​‌Physical Review Research8​​013070January 2026HAL​​​‌DOI
• 22 articleL.​Lewis Wooltorton, P.​‌Peter Brown and R.​​Roger Colbeck. Expanding​​​‌ bipartite Bell inequalities for​ maximum multi-partite randomness.​‌Quantum9December 2025​​, 1930HALDOI​​​‌
• 23 articleL.Lewis​ Wooltorton, P.Peter​‌ Brown and R.Roger​​ Colbeck. Genuine Multipartite​​​‌ Entanglement is Not Necessary​ for Standard Device-Independent Conference​‌ Key Agreement.Physical​​ Review Letters13522​​​‌November 2025, 220803​HALDOI

International peer-reviewed​‌ conferences

• 24 inproceedingsA.​​ A.Alastair A. Abbott​​​‌, M.Mehdi Mhalla​ and P.Pierre Pocreau​‌. Classical and Quantum​​ Query Complexity of Boolean​​​‌ Functions under Indefinite Causal​ Order.Electronic Proceedings​‌ in Theoretical Computer Science​​QPL 2025 - 22nd​​​‌ International Conference on Quantum​ Physics and Logic426​‌Varna, BulgariaAugust 2025​​, 270-300HALDOI​​​‌back to text
• 25​ inproceedingsA.Arthur Mehta​‌, C.Connor Paddock​​ and L.Lewis Wooltorton​​​‌. Self-Testing in the​ Compiled Setting via Tilted-CHSH​‌ Inequalities.Leibniz International​​ Proceedings in Informatics (LIPIcs),​​​‌ Volume 350, pp. 8:1-8:19,​ Schloss Dagstuhl – Leibniz-Zentrum​‌ für Informatik (2025)Conference​​ on the Theory of​​​‌ Quantum Computation, Communication and​ Cryptography (TQC)350Bengaluru​‌ (India), IndiaSchloss Dagstuhl​​ – Leibniz-Zentrum für Informatik​​​‌2025, 8:1-8:19HAL​DOI
• 26 inproceedingsC.​‌Cambyse Rouzé, D.​​ S.Daniel Stilck França​​​‌ and Á.Álvaro Alhambra​. Efficient Thermalization and​‌ Universal Quantum Computing with​​ Quantum Gibbs Samplers.​​​‌STOC '25: Proceedings of​ the 57th Annual ACM​‌ Symposium on Theory of​​ ComputingSTOC 2025 -​​​‌ 57th Annual ACM Symposium​ on Theory of Computing​‌Prague Czechia, Czech Republic​​ACMJune 2025,​​​‌ 1488-1495HALDOI

Conferences​ without proceedings

• 27 inproceedings​‌M.Mario Berta,​​ M. X.Michael X​​​‌ Cao, H.-C.Hao-Chung​ Cheng, O.Omar​‌ Fawzi, A.Aadil​​ Oufkir and Y.Yongsheng​​​‌ Yao. Channel Simulation:​ Tight meta converse for​‌ error and strong converse​​ exponents.QIP 2025​​​‌ - 28th Annual Quantum​ Information Processing ConferenceRaleigh​‌ (NC), United States2025​​HAL
• 28 inproceedingsM.​​​‌Matthias Christandl, O.​Omar Fawzi and A.​‌Ashutosh Goswami. Fault-tolerant​​ quantum input/output.QIP​​​‌ 2025 - 28th Quantum​ Information Processing ConferenceRaleigh​‌ (NC), United States2025​​, 1-80HALback​​ to text
• 29 inproceedings​​​‌N.Nilanjana Datta,‌ O.Omar Fawzi,‌​‌ M.Mizanur Rahaman,​​ S.Satvik Singh and​​​‌ M.Mostafa Taheri.‌ Information transmission under Markovian‌​‌ noise.QIP 2025​​ - 28th international conference​​​‌ on Quantum Information Processing‌Raleigh (NC), United States‌​‌2025, 1-14HAL​​DOI
• 30 inproceedingsK.​​​‌Kun Fang, H.‌Hamza Fawzi and O.‌​‌Omar Fawzi. Generalized​​ quantum asymptotic equipartition.​​​‌QIP 2025 - 28th‌ Annual Quantum Information Processing‌​‌ ConferenceRaleigh Convention Center​​ Raleigh, NC, United States​​​‌2025HAL
• 31 inproceedings‌O.Omar Fawzi,‌​‌ J.Jan Kochanowski,​​ C.Cambyse Rouzé and​​​‌ T.Thomas van Himbeeck‌. Additivity and chain‌​‌ rules for quantum entropies​​ via multi-index Schatten norms​​​‌.TQC 2025 -‌ Theory of Quantum Computation,‌​‌ Communication and CryptographyBangalore,​​ India2025HAL
• 32​​​‌ inproceedingsO.Omar Fawzi‌, A.Aadil Oufkir‌​‌ and R.Robert Salzmann​​. Optimal Fidelity Estimation​​​‌ from Binary Measurements for‌ Discrete and Continuous Variable‌​‌ Systems.QIP 2025​​ - 28th International conference​​​‌ on Quantum Information Processing‌Raleigh (NC), United States‌​‌2025HAL
• 33 inproceedings​​S. O.Samuel O.​​​‌ Scalet, A.Angela‌ Capel, A. N.‌​‌Anirban N. Chowdhury,​​ H.Hamza Fawzi,​​​‌ O.Omar Fawzi,‌ I. H.Isaac H.‌​‌ Kim and A.Arkin​​ Tikku. Classical Estimation​​​‌ of the Free Energy‌ and Quantum Gibbs Sampling‌​‌ from the Markov Entropy​​ Decomposition.TQC 2025​​​‌Bangalore, India2025HAL‌

Reports & preprints

• 34‌​‌ miscL. E.Lucas​​ Emanuel Antunes Porto,​​​‌ S.Sébastien Designolle,‌ S.Sebastian Pokutta and‌​‌ M. T.Marco Túlio​​ Quintino. Measurement incompatibility​​​‌ and quantum steering via‌ linear programming.2025‌​‌HALDOIback to​​ textback to text​​​‌
• 35 miscA.Andreas‌ Bluhm, M.Matthias‌​‌ Caro, F. E.​​Francisco Escudero Gutiérrez,​​​‌ A.Aadil Oufkir and‌ C.Cambyse Rouzé.‌​‌ Certifying and learning quantum​​ Ising Hamiltonians.2025​​​‌HAL
• 36 miscE.‌ Z.Emmanuel Zambrini Cruzeiro‌​‌, J. R.Junior​​ R. Gonzales-Ureta, R.​​​‌Raman Choudhary, H.‌Hugo Abreu, A.‌​‌Adán Cabello and S.​​Sébastien Designolle. Exploring​​​‌ Bell nonlocality with extremal‌ non-signaling boxes.January‌​‌ 2026HAL
• 37 misc​​I.Idris Delsol,​​​‌ O.Omar Fawzi,‌ L.Li Gao and‌​‌ M.Mizanur Rahaman.​​ Emulation Capacity between Idempotent​​​‌ Channels.December 2025‌HAL
• 38 miscI.‌​‌Idris Delsol, O.​​Omar Fawzi, J.​​​‌Jan Kochanowski and A.‌Akshay Ramachandran. Computational‌​‌ aspects of the trace​​ norm contraction coefficient.​​​‌2025HAL
• 39 misc‌S.Sébastien Designolle.‌​‌ Most incompatible measurements and​​ sum-of-squares optimisation.January​​​‌ 2026HALback to‌ textback to text‌​‌
• 40 miscD.Dawei​​ Ding, Z.Zhengfeng​​​‌ Ji, P.Pierre‌ Pocreau, M.Mingze‌​‌ Xu and X.Xinyu​​ Xu. Quantum Nonlocality​​​‌ under Latency Constraints.‌2025HALDOI
• 41‌​‌ miscO.Omar Fawzi​​, J.Jan Kochanowski​​​‌, C.Cambyse Rouzé‌ and T.Thomas van‌​‌ Himbeeck. Additivity and​​​‌ chain rules for quantum​ entropies via multi-index Schatten​‌ norms.2025HAL​​
• 42 miscC.Carla​​​‌ Ferradini, V.Victor​ Gitton and V.V.​‌ Vilasini. Cyclic functional​​ causal models beyond unique​​​‌ solvability with a graph​ separation theorem.February​‌ 2025HALback to​​ textback to text​​​‌
• 43 miscC.Carla​ Ferradini, V.Victor​‌ Gitton and V.V.​​ Vilasini. Cyclic quantum​​​‌ causal modelling with a​ graph separation theorem.​‌February 2025HALback​​ to textback to​​​‌ text
• 44 miscC.​Cameron Foreman, L.​‌Lewis Wooltorton, K.​​Kevin Milner and F.​​​‌ J.Florian J Curchod​. An efficient construction​‌ of Raz's two-source randomness​​ extractor with improved parameters​​​‌.June 2025HAL​
• 45 miscD. S.​‌Daniel Stilck França,​​ T.Tim Möbus,​​​‌ C.Cambyse Rouzé and​ A.Albert Werner.​‌ Learning and certification of​​ local time-dependent quantum dynamics​​​‌ and noise.2025​HAL
• 46 miscM.​‌Maarten Grothus, A.​​ A.Alastair A. Abbott​​​‌, A.Augustin Vanrietvelde​ and C.Cyril Branciard​‌. Routing Quantum Control​​ of Causal Order.​​​‌2025HALback to​ text
• 47 miscT.​‌Timothee Hoffreumon and M.​​Mischa Woods. Quantum​​​‌ theory does not need​ complex numbers.April​‌ 2025HALDOI
• 48​​ miscE.Eliot Jean​​​‌, R.Ralph Silva​ and V.V. Vilasini​‌. An equivalence between​​ time-symmetry and cyclic causality​​​‌ in quantum theory.​August 2025HALback​‌ to text
• 49 misc​​J.Jan Kochanowski,​​​‌ O.Omar Fawzi and​ C.Cambyse Rouzé.​‌ Complexity of mixed Schatten​​ norms of quantum maps​​​‌.2025HAL
• 50​ miscY.-C.Ye-Chao Liu​‌, J.Jannis Halbey​​, S.Sebastian Pokutta​​​‌ and S.Sébastien Designolle​. A unified toolbox​‌ for multipartite entanglement certification​​.2025HALDOI​​​‌back to textback​ to text
• 51 misc​‌R.Raphaël Mothe,​​ A. A.Alastair A.​​​‌ Abbott and C.Cyril​ Branciard. Correlations and​‌ quantum circuits with dynamical​​ causal order.2025​​​‌HALDOIback to​ text
• 52 miscN.​‌Nuriya Nurgalieva and V.​​V. Vilasini. Any​​​‌ theory that admits a​ Wigner's Friend type multi-agent​‌ paradox is logically contextual​​.February 2025HAL​​​‌back to textback​ to text
• 53 misc​‌S.Sujit Rao.​​ A convergent hierarchy of​​​‌ spectral gap certificates for​ qubit Hamiltonians.October​‌ 2025HAL
• 54 misc​​ C.Carlos Vieira,​​​‌ C.Carlos de Gois​, P.Pedro Lauand​‌, L. E.Lucas​​ Emanuel Antunes Porto,​​​‌ S.Sébastien Designolle and​ M. T.Marco Túlio​‌ Quintino. Can outcome​​ communication explain Bell nonlocality?​​​‌ 2025 HAL DOI back​ to text
• 55 misc​‌V.V. Vilasini,​​ L.-Q.Lin-Qing Chen,​​​‌ L.Liuhang Ye and​ R.Renato Renner.​‌ Events and their Localisation​​ are Relative to a​​​‌ Lab.May 2025​HALback to text​‌
• 56 miscV.V.​​ Vilasini and R.Roger​​​‌ Colbeck. The standard​ no-signalling constraints in Bell​‌ scenarios are neither sufficient​​ nor necessary for preventing​​ superluminal signalling with general​​​‌ interventions.2025HAL‌