2025Activity report​​​‌Project-TeamQURIOSITY

3.1.1 Everlasting security​ from a quantum-computational hybrid​‌ model

We proposed in​​ 2015 a security model​​​‌ that we later coined​ a Quantum Computational Timelock​‌ (QCT) security model. It​​ consists in assuming that​​​‌ computationally secure encryption may​ only be broken after​‌ time much longer than​​ the coherence time of​​​‌ quantum memories available at​ the time of protocol​‌ execution. The QCT security​​ model opens the possibility​​​‌ to propose new quantum​ cryptographic constructions and in​‌ particular to make use​​ of encoding and security​​​‌ proof techniques that strongly​ depart from “traditional” quantum​‌ conjugate coding that is​​ a central ingredient in​​​‌ most quantum cryptographic protocols.​

Description of the QCT​‌ security model

The QCT security​​​‌ model opens towards a​ rich variety of fascinating​‌ questions, that we have​​ certainly not all identified.​​​‌ In the coming years​ we intend to push​‌ forward the theoretical analysis​​ of several of these​​​‌ questions, that relate to​ the computational frontiers of​‌ quantum cryptography. One ongoing​​ direction consists in studying​​​‌ key agreement constructions whose​ security can be reduced​‌ to distributed computational problems​​ that exhibit an exponential​​​‌ separation in terms of​ quantum or classical communication​‌ complexity.

As an alternative​​ way to build secure​​​‌ protocols in the QCT​ model, we also intend​‌ to investigate pseudo-random quantum​​ states, which can​​​‌ be seen as a​ computational variant of a​‌ $t$-design, i.e. an​​ ensemble of quantum states​​​‌ characterized by the fact​ that $t$ copies of​‌ one sampled state are​​ statistically indistinguishable from $\mathrm{t‌}$ copies of a states​ picked uniformly at random.​‌ Interestingly, construction of pseudo-random​​ states can be based​​​‌ on quantum-secure one-way functions,​ and therefore from the​‌ first assumption. This line​​ of work will also​​​‌ allow us to consider​ realistic and pratical constructions​‌ of quantum cryptographic schemes​​ based on computational and​​​‌ /or quantum-hardware security assumptions.​ We also intend to​‌ study constructions for quantum​​ physically uncloneable functions qPUFs​​​‌ and their aplication.

3.1.2​ Device-independent cryptography

Device-independent cryptography​‌ allows one to perform​​ quantum cryptography with reduced​​​‌ or even no trust​ assumptions on the quantum​‌ hardware. It remains a​​ challenge experimentally and pushing​​​‌ the performance (in terms​ of key rate, or​‌ trust reduction) of device-independent​​ cryptography defines an active​​​‌ research frontier for quatum​ cryptography. Recent implementations of​‌ DI-QKD179,​​ 93, 93 have​​​‌ shown that whilst it​ is now feasible, it​‌ has a relatively low​​ rate and can only​​​‌ be executed over a​ short distance. By improving​‌ the theoretical methods for​​ analyzing various protocols and​​​‌ security proofs and by​ improving the protocol design​‌ we can look to​​ boost the rates of​​ these protocols and push​​​‌ them towards a more‌ viable technology. Examples of‌​‌ such improvements include protocol​​ design modifications 87,​​​‌ 70 and improved methods‌ to calculate rates 56‌​‌, 57, 86​​. Our goals are​​​‌ to develop better designed‌ protocols and security proofs‌​‌ (assessing their performance in​​ experiments) and to investigate​​​‌ the fundamental limitations of‌ DI protocol rates Overall‌​‌ pushing the practicality of​​ DI forwards and improving​​​‌ our understanding of its‌ limitations.

As a complementary‌​‌ line of research we​​ will also investigate prospects​​​‌ of semi-device-independent protocols as‌ a viable near-term alternative‌​‌ to device-independent security. Proposed​​ protocols rely on assumptions​​​‌ of system energy 85‌, dimension bounds and‌​‌ bounded distrust 88 amongst​​ others. We will investigate​​​‌ alternative assumptions and derive‌ resulting protocols to be‌​‌ analyzed and subsequently implemented.​​ We will also apply​​​‌ the semi-device-independent framework to‌ the problem of hardware‌​‌ verification, designing tests to​​ establish that the hardware​​​‌ is functioning correctly whilst‌ placing limited trust on‌​‌ the components.

3.1.3 Quantum-enhanced​​ leakage-resilience

We will also​​​‌ investigate some questions placed‌ at the intersection between‌​‌ classical hardware security and​​ quantum cryptography, namely how​​​‌ to prove the security‌ of a cryptographic protocols‌​‌ when implemented using hardware,​​ such as processors or​​​‌ storage, that may leak‌ some of the security-sensitive‌​‌ information.

We intend to​​ tackle leakage-resilience cryptography from​​​‌ a new viewpoint, that‌ will consist in integrating‌​‌ quantum cryptographic constructions as​​ a base layer within​​​‌ cryptographic systems, in order‌ to obtain security guarantees‌​‌ even in presence of​​ information leakage with strictly​​​‌ weaker assumptions than existing‌ classical leakage-resilience protocols. We‌​‌ will first consider simple​​ cryptographic protocols such as​​​‌ One-Time-Pad encryption or authentication‌ protocols relying on Physically‌​‌ Uncloneable Functions PUFs. We​​ intend for example to​​​‌ investigate how the use‌ of hybrid classical-quantum cryptographic‌​‌ hardware, comprising quantum channels​​ to interconnect processors or​​​‌ secure storage sites, can‌ lead to cryptographic protocols‌​‌ with provable security under​​ some realistic information leakage​​​‌ models.

3.1.4 Real-world quantum‌ cryptography

40 year of‌​‌ quantum cryptography (QC) have​​ lead to major theoretical​​​‌ and technological advances, with‌ fundamental impact on the‌​‌ field of information security.​​ Market adoption however remains​​​‌ limited, with major challenges‌ that practical QC still‌​‌ needs to be overcome​​ in order to become​​​‌ widely used in real-world‌ applications. We identify in‌​‌ particular two main challenges:​​ 1) cryptographic advantage, namely​​​‌ the design of protocols‌ for which the use‌​‌ of QC in combination​​ with classical cryptography gives​​​‌ a competitive edge over‌ classical cryptography only; 2)‌​‌ security certification of quantum​​ cryptographic implementations. Quriosity intends​​​‌ to actively contribute to‌ lift these barriers and‌​‌ to foster the development​​ of real-world quantum cryptography​​​‌ and in particular to‌ the uptake of a‌​‌ French and European industry.​​ The development of a​​​‌ QC industry is indeed‌ becoming an important topic,‌​‌ with strategic investments from​​ leading scientific countries (China,​​​‌ Korea, Japan, UK, etc.‌ ) including also notably‌​‌ the EU27 supporthing the​​ EuroQCI initiative. On the​​​‌ other hand, the adoption‌ of quantum cryptography for‌​‌ real-world application remains often​​​‌ considered with skepticism by​ representatives of the cybersecurity​‌ community, stressing the dire​​ need of cross-disciplinary vision​​​‌ combining best-in-class classical and​ quantum cryptography expertise.

Regarding​‌ cryptographic advantage, our conviction​​ is that one should​​​‌ not aim at constructions​ where quantum cryptography would​‌ just functionally replace classical​​ cryptography, but on the​​​‌ other hand to identify​ applications where the use​‌ of QC combined with​​ post-quantum cryptography (PQC) can​​​‌ present strict security gain​ over PQC alone.

Regarding​‌ security certification, it has​​ become a central challenge​​​‌ in particular in the​ context of the EuroQCI​‌ initiative aiming at developing​​ a pan-European quantum communication​​​‌ infrastructure, together with an​ industry, in the next​‌ 10 years It constitutes​​ a complex task, requiring​​​‌ the collaboration of experts​ from different fields. In​‌ future years, we intend​​ to tackle this question​​​‌ from different angles: on​ the theory side, we​‌ intend to propose a​​ shift in the security​​​‌ objective towards everlasting security,​ and demonstrate how this​‌ can make the security​​ certification of key establishment​​​‌ based on QKD combined​ with ephemeral post-quantum cryptography​‌ primitives much more tractable.​​ On the system engineering​​​‌ side and in resonance​ with Section 3.2,​‌ we intend to identify​​ and close implementation security​​​‌ gaps in modern CV-QKD​ systems relying on digital​‌ signal processing, notably the​​ complex interplay between calibration​​​‌ procedure and finite-size security,​ but also between Nyquist​‌ pulse shaping and leakage.​​

3.2.1 Quantum​ coherent communications and digital​‌ signal processing

Quantum Key​​ Distribution (QKD) systems are​​​‌ among the most advanced​ quantum communications technologies available​‌ today. QKD therefore provides​​ an ideal platform to​​​‌ test novel system designs​ and validate quantum communication​‌ technology over real networks​​ Leveraging essential features of​​​‌ modern optical communication systems,​ and in particular high​‌ sampling rates and digital​​ signal processing 74,​​​‌ quantum coherent communications systems​ constitute a recent and​‌ promising route towards high-rates,​​ highly integrated and cost-effective​​​‌ quantum communication systems. They​ rely on two central​‌ ingredients: -Spectrally efficient modulation​​ formats and coherent detection,​​​‌ exploiting phase and intensity​ information and able to​‌ operate a very high​​ rates (> GHz) even​​​‌ with shot-noise limited receivers.​ - Digital signal processing​‌ that takes advantage of​​ the high sampling rates​​​‌ to digitally evaluate and​ compensate many impairments of​‌ the communications such as​​ optical carrier phase noise​​ or polarization mode dispersion,​​​‌ using dedicated algorithms.

In‌ collaboration with Prof. Yves‌​‌ Jaouen from the GTO​​ team of Telecom Paris,and​​​‌ working on a state-of-the-art‌ experimental platform, Quriosity has‌​‌ designed and demonstrated for​​ the first time DSP-enhanced​​​‌ quantum communications, with noise‌ control performances that allow‌​‌ to successfully run QKD​​ over metropolitan distances while​​​‌ being jointly deployed over‌ classical coherent optical link‌​‌ 50. We have​​ also filed a patent​​​‌ about this general concept‌ and our inventive system‌​‌ design.

In the future,​​ we then aim to​​​‌ leverage digital signal processing‌ and machine learning (ML)‌​‌ techniques to characterize and​​ mitigate noise in order​​​‌ to push further our‌ ability to operate quantum‌​‌ communications over existing optical​​ fibers, in coexistence with​​​‌ classical signals.

As a‌ complementary line of research,‌​‌ we intend to theoretically​​ study multimode quantum coherent​​​‌ communications using multimode shaping‌ of the local oscillator,‌​‌ taking inspiration from 58​​. We also intend​​​‌ to explore the possibility‌ to rely on CV‌​‌ multimode encoding as a​​ way to experimentally implement​​​‌ new quantum cryptographic constructions‌ in the hybrid quantum‌​‌ computational security models introduced​​ in Section 3.1.​​​‌

3.2.2 Quantum information processing‌ with a programmable frequency‌​‌ processor

In collaboration with​​ the teams of Nadia​​​‌ Belabas and Pascale Senellart‌ at C2N and in‌​‌ the context of the​​ ParisQCI project, we study​​​‌ how to combine high-dimensional‌ photonic gates in the‌​‌ frequency domain, to efficiently​​ synthesize high-dimensional unitary transformations.​​​‌ Leveraging on the possibility‌ to parallelize single-qubit unitaries,‌​‌ that we have recently​​ analyzed 71 we intend​​​‌ to study how such‌ systems could be leveraged‌​‌ for optical quantum information​​ processing, and in particular​​​‌ for quantum metrology. In‌ the future, we will‌​‌ also investigate how to​​ scale the platform to​​​‌ perform information processing with‌ high-dimensional quantum states, opening‌​‌ the possibility to achieve​​ quantum computational advantage, but​​​‌ also implementation routes for‌ the hybrid quantum-computational cryptographic‌​‌ protocols in the QCT​​ model, studied in Section​​​‌ 3.1

Multimode programmable linear‌ optical circuit and associated‌​‌ experimental devices (Spatial Light​​ Modulators: SLM, Multimode fibers:​​​‌ MMF, Detection of single‌ photons multipixel APDs).

3.2.3 Quantum​​​‌ information processing using multimode‌ programmable linear circuits

In‌​‌ collaboration with the team​​ of Sylvain Gigan at​​​‌ ENS Ulm, and in‌ the context of Francesco‌​‌ Mazzoncini's PhD that we​​ co-supervise, we aim to​​​‌ use a multimode programmable‌ linear circuit, built around‌​‌ a multimode fiber (cf.​​ Figure 2) to​​​‌ perform some fundamental tests‌ and demonstrations of quantum‌​‌ communication advantage, related to​​ fundamental problems such as​​​‌ the Vector in a‌ Subspace 81.

The‌​‌ prospects of this work​​​‌ are very promising: first​ they could lead to​‌ the first experimental demonstration​​ of a exponential communication​​​‌ complexity gap between one-way​ quantum communication and two-way​‌ classical communications and may​​ also open towards the​​​‌ possibility for experimentally robust​ Bell inequality violations 76​‌, with applications for​​ quantum cryptography and also​​​‌ in quantum computing.

3.2.4​ Photonic Noise Correction in​‌ Fault-Tolerant Quantum Systems

In​​ collaboration with Quandela and​​​‌ as part of Katia​ Hakem's CIFRE PhD thesis,​‌ this project aims to​​ develop adaptive fault-tolerant architectures​​​‌ tailored to photonic quantum​ systems. Traditional quantum error​‌ correction (QEC) frameworks often​​ fail to address photonic-specific​​​‌ errors such as photon​ loss, impurity, and distinguishability.​‌ Our approach focuses on​​ accurately modeling the propagation​​​‌ of these errors in​ linear-optical systems and designing​‌ correction protocols that leverage​​ the heralded nature of​​​‌ most photonic errors. By​ integrating feedforward mechanisms, we​‌ seek to optimize resource​​ efficiency and performance. This​​​‌ work is critical not​ only for photonic quantum​‌ computing but also for​​ hybrid and distributed quantum​​​‌ platforms, where photonic links​ are often considered bottleneck​‌ for scalability.

3.2.5 Efficient​​ Generation of Photonic Graph​​​‌ States

Graph states are​ a fundamental resource for​‌ quantum information technologies, enabling​​ advancements in sensing, communication,​​​‌ and computing. This project​ focuses on developing resource-optimized​‌ protocols for generating photonic​​ graph states, with an​​​‌ emphasis on minimizing photon​ and operational overhead. We​‌ will first explore hardware-agnostic​​ heuristics to identify universally​​​‌ applicable generation techniques, then​ specialize these protocols for​‌ photonic systems. By reducing​​ resource demands, this work​​​‌ will accelerate the deployment​ of graph states in​‌ quantum algorithms and fault-tolerant​​ architectures, bridging the gap​​​‌ between theoretical potential and​ experimental feasibility.

3.2.6 Development​‌ of Early-Fault Tolerant Quantum​​ Computing

Current quantum hardware​​​‌ is limited by noise,​ yet full fault tolerance​‌ remains resource-prohibitive. This project​​ explores early-fault tolerant schemes​​​‌ - partial error correction​ strategies that reduce noise​‌ without the overhead of​​ full fault tolerance. By​​​‌ identifying regimes where noise​ is sufficiently suppressed to​‌ enable quantum advantage, we​​ aim to unlock practical​​​‌ applications on near-term devices.​ This approach could serve​‌ as a critical stepping​​ stone, offering tangible benefits​​​‌ in algorithm performance and​ system reliability while paving​‌ the way for fully​​ fault-tolerant quantum computing.

3.3.1​​​‌ Convex relaxations of quantum​ optimization problems

Convex optimization​‌ concerns the optimization of​​ convex functions over convex​​ sets. This family of​​​‌ optimization problems has several‌ particularly nice properties, including‌​‌ the guarantee of global​​ optima, which makes them​​​‌ particularly appealing from both‌ the perspective of the‌​‌ mathematics and the applications.​​ They are widely applicable​​​‌ to many domains of‌ science but in particular‌​‌ they arise rather naturally​​ in the context of​​​‌ quantum theory as many‌ of the relevant objects‌​‌ (states, channels and measurements)​​ form convex sets.

We​​​‌ will aim to develop‌ and apply techniques in‌​‌ convex optimization theory to​​ problems within quantum information​​​‌ and quantum computing. Recent‌ examples of our work‌​‌ in this area include​​ 56, 57 where​​​‌ we developed semidefinite programming‌ relaxations for entropic optimization‌​‌ problems relevant to device​​ independent cryptography. Continuing this​​​‌ line of research we‌ aim to extend these‌​‌ techniques to other entropic​​ quantities beyond the relative​​​‌ entropy, for instance to‌ the Petz and sandwiched‌​‌ families of Rényi divergences.​​ We also have the​​​‌ ambitious goal of understanding‌ and characterizing what classes‌​‌ of functions, relevant in​​ the context of quantum​​​‌ theory, are amenable to‌ such semidefinite programming approximations.‌​‌ In other words, what​​ optimization problems in quantum​​​‌ information theory and quantum‌ computing can we approximate?‌​‌

A well-known example concerns​​ strengthenings of the monotonicity​​​‌ of the relative entropy‌ under the action of‌​‌ a quantum channel or​​ a Markovian evolution known​​​‌ as strong data processing‌ and modified logarithmic Sobolev‌​‌ inequalities. These fundamental inequalities​​ are known to be​​​‌ hard to prove analytically,‌ even for simple random‌​‌ walks on $n$-cycles,​​ and convex relaxation techniques​​​‌ were recently successfully used‌ to approximate them 66‌​‌. We are currently​​ collaborating with Omar Fawzi​​​‌ and Daniel Stilck França‌ from QINFO to adapt‌​‌ these numerical tools to​​ the quantum realm. In​​​‌ the future, we will‌ consider extending these tools‌​‌ to the infinite dimensional​​ bosonic setting in order​​​‌ to approach long-standing conjectures‌ such as the entropy‌​‌ photon number inequality 69​​. This research direction​​​‌ will complement analytic approaches‌ presented in Section 3.3.2‌​‌.

3.3.2 Fundamental properties​​ of entropies

Entropies are​​​‌ fundamental quantities in quantum‌ information theory, obtaining operational‌​‌ meanings in terms of​​ rates of various tasks​​​‌ 65. By improving‌ our understanding of these‌​‌ quantities, we can in​​ turn gain new insights​​​‌ into the various applications‌ in which they appear.‌​‌

For example, new chain​​ rules for Rényi entropies​​​‌ 64 led to a‌ versatile framework for cryptographic‌​‌ security proofs 49.​​ The result, known as​​​‌ the entropy accumulation theorem,‌ effectively gives sufficient conditions‌​‌ under which the entropy​​ of a large system​​​‌ can be accurately described‌ by the entropy of‌​‌ its individual systems. At​​ QURIOSITY we aim to​​​‌ understand under which conditions‌ does entropy accumulate in‌​‌ this manner? By understanding​​ the minimal requirements for​​​‌ entropy to accumulate we‌ can understand the minimal‌​‌ requirements under which a​​ randomness based cryptographic protocol​​​‌ functions securely. Moreover, we‌ aim to investigate the‌​‌ connection between the entropy​​ accumulation theorem and the​​​‌ related works of the‌ quantum probability estimation framework‌​‌ 92. This is​​​‌ an alternative method to​ break large entropies down​‌ into smaller quantities and​​ reports several advantages over​​​‌ the entropy accumulation theorem.​ Understanding how advantages from​‌ one technique can be​​ transferred to the other​​​‌ will lead to much​ stronger theoretical results and​‌ would have immediate applications​​ to improve security proofs​​​‌ and rates of cryptographic​ protocols, leading to more​‌ practical technologies.

Other types​​ of decompositions of entropic​​​‌ quantities of interacting complex​ systems into smaller components​‌ involving marginals over subsystems​​ include generalizations of the​​​‌ famous strong subadditivity of​ the relative entropy known​‌ as approximate tensor-stability of​​ the relative entropy. These​​​‌ are at the core​ of most successful methods​‌ for finding the speed​​ of convergence of Gibbs​​​‌ sampling algorithms based on​ the modified logarithmic Sobolev​‌ inequality. In previous work,​​ we successfully extended these​​​‌ notions to the quantum​ realm 68 and applied​‌ them to problems in​​ network quantum information theory​​​‌ 54, 62 and​ open complex quantum systems​‌ 59, 51.​​ Extensions and refinements of​​​‌ these concepts will lead​ to new breakthroughs in​‌ both fields (see Sections​​ 3.3.3 and 3.3.4).​​​‌

3.3.3 Complexity and entanglement​ properties of quantum Gibbs​‌ states

A complexity theoretical​​ definition of the quantum​​​‌ phase of a state​ $\psi$ consists in taking​‌ the vicinity of states​​ which are reachable from​​​‌ $\psi$ after applying a​ local evolution during a​‌ short period of time.​​ A topologically ordered phase​​​‌ has the property that​ the time required to​‌ reach it starting from​​ a trivial (i.e. product)​​​‌ state scales extensively with​ the system size. In​‌ other words, topological order​​ can be described in​​​‌ terms of circuit depth​ lower bounds. The classification​‌ of quantum phases of​​ matter is by now​​​‌ a very well-established field​ with far-reaching applications e.g.​‌ to the construction of​​ good quantum error-correcting codes​​​‌ exploiting the properties of​ topologically ordered phases. However,​‌ a more realistic description​​ of a quantum mechanical​​​‌ system is in terms​ of a finite temperature​‌ Gibbs state describing its​​ thermal equilibrium with a​​​‌ large environment. Despite their​ practical relevance, until recently​‌ Gibbs states were primarily​​ studied by mathematical physicists,​​​‌ and many fundamental questions​ regarding their use in​‌ quantum information processing remain​​ open. We propose to​​​‌ investigate the complexity of​ quantum Gibbs states through​‌ the scope of their​​ finite temperature phase transitions.​​​‌ Additionally to its fundamental​ value, this research direction​‌ will undoubtedly lead to​​ several important practical applications,​​​‌ as described in section​ 3.3.4.

In the​‌ setting of classical Gibbs​​ measures, analogous questions have​​​‌ been intensively studied from​ the perspective of Markov​‌ chain Monte Carlo algorithms​​ (MCMC). On regular lattices,​​​‌ the analysis of the​ speed of convergence of​‌ MCMC for lattice spin​​ systems is by now​​​‌ well-understood through the study​ of correlations at equilibrium.​‌ The generalization to general​​ interaction graphs is still​​​‌ a very active field​ of research in theoretical​‌ computer science, probability theory​​ and mathematical physics 60​​​‌. The problem becomes​ even harder in the​‌ quantum regime, where purely​​ quantum mechanical effects, e.g.​​ long-range entanglement, may cause​​​‌ the quantum Markov chain‌ to slow down in‌​‌ an unpredicted manner. For​​ the important case of​​​‌ commuting interactions, which include‌ most hitherto studied Hamiltonians‌​‌ for the purpose of​​ quantum error-correction, and for​​​‌ physical dynamics generated by‌ the weak coupling of‌​‌ the system with a​​ large environment (Davies dynamics),​​​‌ general results were obtained‌ through spectral methods. However‌​‌ the latter are not​​ powerful enough to distinguish​​​‌ evolutions generating topologically ordered‌ states from rapidly mixing‌​‌ ones. Instead, more involved​​ techniques, e.g. entropic inequalities,​​​‌ are needed. In 53‌, 59, 52‌​‌, 51, we​​ were able to prove​​​‌ rapid mixing by extending‌ one of the most‌​‌ successful classical approaches to​​ prove rapid mixing based​​​‌ on the modified logarithmic‌ Sobolev inequality and the‌​‌ approximate tensor-stability of the​​ relative entropy (cf Section​​​‌ 3.3.2). Extending this‌ novel powerful approach, we‌​‌ plan to conduct a​​ systematic joint study of​​​‌ mixing times and thermal‌ stability of topological quantum‌​‌ order in low lattice​​ dimensions. We will conduct​​​‌ this research in collaboration‌ with Daniel Stilck França‌​‌ from QINFO with whom​​ we co-authored 59.​​​‌ We also see a‌ clear connection with the‌​‌ research focus of Daniel​​ Malz who was recently​​​‌ recruited as a junior‌ professor at Inria Saclay,‌​‌ the mathematical and theoretical​​ condensed matter physicists at​​​‌ CPhT, as well as‌ the team PEIPS at‌​‌ CMAP (X).

3.3.4 Mathematical​​ analysis of quantum memories​​​‌

In parallel to the‌ previous research plan, we‌​‌ will conduct a mathematical​​ analysis on the storage​​​‌ of quantum information and‌ the concept of self-correction‌​‌ in complex quantum systems.​​ Early work on the​​​‌ storage time of candidates‌ of self-correcting quantum memories‌​‌ relied on the connection​​ to the energy barrier​​​‌ of the system, that‌ is the energy the‌​‌ system must reach for​​ a logical error to​​​‌ occur, via an empirical‌ principle called the Arrhenius‌​‌ law. More recently, the​​ energy barrier was rigorously​​​‌ related to spectral properties‌ of the evolution, whereas‌​‌ some no-go theorems showed​​ the impossibility of an​​​‌ exact mathematical formulation of‌ the Arrhenius law. Here‌​‌ instead, we plan to​​ relate the memory lifetime​​​‌ of a device directly‌ to properties of its‌​‌ thermal equilibrium state. We​​ currently work on this​​​‌ research direction in the‌ setting of lattice spin‌​‌ systems with Anthony Leverrier​​ and Ivan Bardet from​​​‌ the team COSMIQ through‌ the development of spectral‌​‌ methods, and plan to​​ extend our framework to​​​‌ lattices with bosonic degrees‌ of freedom in the‌​‌ near future. We also​​ plan to initiate a​​​‌ dialogue with Jean-René Chazottes‌ from CPhT (X) on‌​‌ refinements of our techniques​​ using concentration and entropic​​​‌ inequalities which already proved‌ their usefulness in the‌​‌ study of hitting times​​ of classical Markov chains​​​‌ and their metastability. One‌ of our long–term goals‌​‌ is to find systems​​ with thermally stable entanglement,​​​‌ both stable against thermal‌ fluctuations and robust against‌​‌ local perturbations. Such a​​ theoretical result would be​​​‌ of very high practical‌ interest since experimental implementations‌​‌ are inevitably subject to​​​‌ noise and errors.

3.3.5​ Tomography of complex quantum​‌ systems

As the size​​ of quantum devices continues​​​‌ to increase beyond what​ can be easily simulated​‌ classically, new challenges have​​ appeared concerning the robust​​​‌ and efficient characterization of​ their states. This often​‌ necessitates the preparation and​​ destructive measurement of exponentially​​​‌ many copies of the​ quantum system, as well​‌ as the storage of​​ measurement outcomes in a​​​‌ classical memory. Recently, new​ methods of tomography have​‌ been proposed which precisely​​ leverage this important simplification​​​‌ to develop efficient state​ learning algorithms. One highly​‌ relevant development in this​​ direction is that of​​​‌ classical shadows 72,​ 73. In we​‌ propose a better solution​​ by combining classical shadows​​​‌ with new insights from​ the emerging field of​‌ quantum optimal transport. Our​​ current first step only​​​‌ applies to topologically trivial​ quantum states such as​‌ high-temperature Gibbs states or​​ outputs of shallow quantum​​​‌ circuits, and more effort​ is needed to adapt​‌ and generalize our algorithm​​ to non-trivial phases. We​​​‌ envision three new major​ contributions: First, we will​‌ develop constrained versions of​​ concentration inequalities in order​​​‌ to develop efficient tomography​ algorithms of complex quantum​‌ states, assuming the prior​​ knowledge of their phase.​​​‌ This line of research​ is original even in​‌ the classical setting where​​ works on constrained entropic​​​‌ inequalities only very recently​ appeared in the literature.​‌ The expertise of Jean-René​​ Chazottes from CPhT (X)​​​‌ will prove crucial to​ the success of this​‌ project. Second, we will​​ extend the framework of​​​‌ shadow tomography to CV​ quantum systems. The main​‌ difficulties here are two-fold:​​ first, CV systems are​​​‌ infinite-dimensional in nature, and​ hence some physical constraints​‌ need to be imposed​​ on the states that​​​‌ one can hope to​ learn, such as their​‌ energy. Moreover, the set​​ of measurements (homodyne/heterodyne) available​​​‌ in photonic experiments further​ limits the type of​‌ observables that one can​​ hope to predict. In​​​‌ order to ensure the​ wide applicability of the​‌ method and test the​​ resulting algorithm, we will​​​‌ rely on the already​ established interactions of IQA​‌ with the groups of​​ experimentalists at IP Paris​​​‌ and Saclay, and initiate​ a fruitful dialogue with​‌ start-up like Quandela and​​ Pasqal. In the future,​​​‌ we will use these​ methods to devise hardware-oriented​‌ noise-learning algorithms for many-body​​ systems. For this, we​​​‌ plan to get in​ touch with the experts​‌ on statistical learning among​​ IP Paris, and in​​​‌ particular at LIX.

3.3.6​ Formal tools for higher-order​‌ quantum computation

The theoretical​​ study of quantum computation​​​‌ and its advantages has,​ in the past decade,​‌ opened to a new​​ perspective: higher-order quantum computation,​​​‌ i.e. the way in​ which one can transform​‌ black-box quantum gates by​​ inserting them into computation​​​‌ architectures. This is useful​ to study the ways​‌ in which one can​​ query subroutines in quantum​​​‌ computation, a pratice that​ is bound to become​‌ ubiquitous, for example in​​ delegated quantum computing. The​​​‌ study of higher-order quantum​ computation has already led​‌ to promising as well​​ as disconcerting results, such​​ as about the difficulty​​​‌ of formally defining a‌ quantum version of the‌​‌ computational `if' clause 48​​, or the fact​​​‌ that one might be‌ able to query two‌​‌ unknown gates in a​​ `superposed order of application',​​​‌ using a computation architecture‌ called the quantum switch‌​‌ 63. Using the​​ latter leads to computational​​​‌ advantages for certain tasks‌ 47. However, the‌​‌ mathematical study of higher-order​​ quantum processes quickly encounters​​​‌ thorny formal issues related‌ to their non-trivial compositional‌​‌ structure.

Overcoming these issues​​ would require the development​​​‌ of a specific and‌ robust type system, stipulating‌​‌ which inputs a given​​ higher-order quantum process admits​​​‌ and which output it‌ produces. Despite recent advances‌​‌ 75, currently available​​ type systems are not​​​‌ detailed enough to provide‌ a fully compositional view‌​‌ of higher-order quantum computation.​​ Our work thus focuses​​​‌ on refining them, through‌ the encoding of sectorial‌​‌ structure, i.e. information about​​ how quantum channels behave​​​‌ with respect to certain‌ direct-sum decompositions of their‌​‌ input and output spaces,​​ using the recently developed​​​‌ framework of routed quantum‌ circuits 89, 90‌​‌. Progress in this​​ direction will pave the​​​‌ way to computer manipulation‌ of complex higher-order processes,‌​‌ for instance to numerically​​ optimise the advantage they​​​‌ yield.

3.3.7 Causal structure‌ in quantum theory

Many‌​‌ of the peculiarities of​​ quantum theory can be​​​‌ tracked down to it‌ not matching our classical‌​‌ notion of causal structure​​ 91; this leads​​​‌ to the question of‌ how one could develop‌​‌ a quantum notion of​​ causal structure, on which​​​‌ some progress has been‌ achieved recently 55.‌​‌ Exploring quantum theory from​​ a causal perspective yields​​​‌ potential progress in understanding‌ its structure and potential‌​‌ applications, in particular for​​ the aforementioned higher-order quantum​​​‌ processes, whose performances are‌ directly connected to their‌​‌ causal structure. In that​​ regard, a particularly important​​​‌ conjecture to prove is‌ that of causal decompositions‌​‌77, which puts​​ forward a tentative equivalence​​​‌ between a unitary channel's‌ causal structure (operational data‌​‌ about which of its​​ inputs can affect which​​​‌ of its outputs) and‌ its compositional structure (mathematical‌​‌ data about how it​​ can be written as​​​‌ the composition of sub-channels).‌ If such a conjecture‌​‌ (which has not been​​ proven yet in the​​​‌ general case) were to‌ be true, it would‌​‌ yield a remarkable mathematical​​ lever on the relationship​​​‌ between the operational and‌ formal sides of quantum‌​‌ theory. We investigate this​​ conjecture mathematically with the​​​‌ aim to prove it‌ in more and more‌​‌ general cases; this involves​​ abstract mathematical methods employing​​​‌ C* algebras. More generally,‌ we explore how the‌​‌ latter might provide a​​ useful formal basis for​​​‌ considerations of causality in‌ a quantum context.

Scientific publication​​

Quriosity aims at publishing​​​‌ high-impact papers in high​ profile journals such as​‌ Nature, Science, Physical Review,​​ Quantum, IEEE Transactions on​​​‌ Information Theory, as well​ as top conferences in​‌ our field such as​​ QIP, QCrypt, TQC as​​​‌ well as Crypto, EuroCrypt,​ CHES.

Innovation

Telecom Paris​‌ currently holds 5 granted​​ patents: 3 on hybrid​​​‌ quantum computational cryptography (axis​ 3.1) and 2​‌ on quantum coherent communications​​ (axis 3.2). We​​​‌ plan to patent technological​ innovations, including foundamental proposals​‌ for which we see​​ a clear implementation route​​​‌ and possible exploitation paths.​

Teaching

  Quriosity intends to​‌ play a vigorous role​​ in the training of​​​‌ the future generation of​ quantum engineers and researchers.​‌ In collaboration with the​​ QuACs Inria team (CentraleSupélec​​​‌ and UPSaclay) and the​ PhiQus Inria team (Ecole​‌ Polytechnique), Quriosity (Telecom Paris-Inria)​​ is coordinating the new​​​‌ M2 master program QMI​ (Quantique, Mathematiques, Informatique) that​‌ has been launched at​​ IP Paris level in​​​‌ september 2025, and is​ the first master program​‌ centered on mathematical and​​ CS aspects of quantum​​​‌ research and technology.

7.1.1​​ 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:
  Peter Johnson Brown‌
• Partners:
  Universidad de Valladolid,‌​‌ University of Siegen, Zuse​​ Institute Berlin

8.1.1 Computational​​​‌ models in quantum cryptography‌

Participants: Romain Alléaume,‌​‌ Peter Brown, Francesco​​ Mazzoncini, Tristan Nemoz​​​‌, Błażej Kuzaka,‌ Jeanne Lucas.

We‌​‌ investigate how computational assumptions​​ can be leveraged quantum​​​‌ cryptographic protocols that keep‌ a strict security advantage,‌​‌ with respect to classical​​ (computational) cryptography, while also​​​‌ allowing to obtain performances‌ and properties that go‌​‌ beyond quantum cryptography in​​ the plain model. To​​​‌ this end we have‌ proposed a key distribution‌​‌ protocol in the so-called​​ Quantum Computational Timelock model,​​​‌ whose security can be‌ based on communication complexity‌​‌ gap between classical and​​ quantum communication 8.​​​‌ In collaboration with LKB‌ (team of Sylvain Gigan)‌​‌ we also proposed a​​ first experimental demonstration of​​​‌ quantum versus classical communicaton‌ two-way complexity advantage.

In‌​‌ the context of the​​ PhD of Tristan Nemoz,​​​‌ we have focused on‌ the mathematical structure and‌​‌ applications of quantum pseudorandom​​ states (PRS), and established​​​‌ a lower bound on‌ the distinguishing probabability between‌​‌ any real-valued PRS and​​ a family of Haar-random​​​‌ states 35. We‌ wrote a general audience‌​‌ article on hybridization of​​ classical and quantum cryptography​​​‌ 5. In parallel,‌ we investigate how PRS‌​‌ security definition could be​​ translated to the practically​​​‌ motivated context of bosonic‌ coherent states (and hence‌​‌ implementable using existing quantum​​ communication systems), and study​​​‌ how to design and‌ prove the security of‌​‌ a key exchange protocol​​ based on PRS, in​​​‌ the QCT model.

8.1.2‌ New results for device-independent‌​‌ cryptography

Participants: Lewis Wooltorton​​, Peter Brown,​​​‌ Roger Colbeck, Thomas‌ Hahn, Ernest Tan‌​‌, Bora Ulu,​​ Nicolas Brunner, Mirjam​​​‌ Weilenmann, Costantino Budroni‌, Miguel Navascués,‌​‌ Aby Philip.

In​​ 30 we develop tight​​​‌ analytical solutions to the‌ finite-size key-rate problem of‌​‌ device-independent cryptography. This vastly​​ simplifies the security proof​​​‌ whilst also improving the‌ achievable rates.

In 14‌​‌ we developed new methods​​ to build multipartite Bell​​​‌ inequalities that certify maximal‌ randomness demonstrating the limits‌​‌ of multipartite device-independent randomness​​ generation. In 15 we​​​‌ solved an open problem‌ recently posed for device-independent‌​‌ conference key agreement protocols,​​​‌ showing that genuinely multipartite​ entanglement is not necessary​‌ to generate secret key​​ – weakening the requirements​​​‌ of these protocols.

We​ have furthermore proposed a​‌ technique to turn setups​​ that do not allow​​​‌ us to prove positive​ key rates for DI-QKD​‌ into setups that do​​ 10. These techniques​​​‌ are based on classical​ pre- and post-processing of​‌ data and can thus​​ in principle be straightforwardly​​​‌ applied to data from​ implementations of current protocols.​‌

In addition, we have​​ proved results on the​​​‌ vulnearbility of protocols in​ networks against memory attacks​‌ 12. This restricts​​ the network topologies in​​​‌ which self-testing and communication​ protocols with quantum advantages​‌ are practically feasible without​​ imposing an i.i.d. assumption.​​​‌

8.2.1 Quantum Coherent​​​‌ Communication and Digital Signal​ Processing

Participants: Romain Alléaume​‌, Gjuillaume Ricard,​​ Nicolas Fabre, Thomas​​​‌ Pousset, Yves Jaouën​, Matteo Schiavon,​‌ Jeanne Lucas, Shivang​​ Srivastava.

In 38​​​‌ we have shown how​ shot noise calibration can​‌ be optimally performed in​​ CV-QKD given some knowledge​​​‌ on the receiver noise​ spectral decomposition.

In 9​‌, we have developped​​ a quantized theory of​​​‌ Kramers-Krönig coherent detection and​ illustrated how it can​‌ be used in quantum​​ communications but also applied​​​‌ to single-photon tomography. We​ are now investigating the​‌ impact of digital signal​​ processing on quantum communications.​​​‌

We moreover contributed to​ the review article 41​‌, accepted for publication​​ in Review of Modern​​​‌ Physcis, writing the section​ on CV-QKD certification.

8.2.2​‌ Quantum Networking

Participants: Romain​​ Alléaume, Thomas Rivera​​​‌, Pierre-Enguerrand Verdier.​

In 11, we​‌ have studied how time​​ multiplexing could be beneficially​​​‌ used as a mean​ to perform long-distance discrete​‌ variable QKD in coexistence​​ with classical communications.

8.2.3​​​‌ Learning bosonic channels

Participants:​ Marco Fanizza, Vishnu​‌ Iyer, Junseo Lee​​, Antonio A. Mele​​​‌, Francesco A. Mele​.

We have initiated​‌ the study of finite-sample​​ size learning of black-box​​​‌ bosonic channels. We considered​ the problem of learning​‌ a Gaussian unitary on​​ $m$ modes and derived​​​‌ rigorous guarantees on the​ number of queries needed​‌ to learn the process​​ accurately in the energy​​​‌ constrained diamond norm distance,​ which is a physically​‌ motivated metric. The algorithm​​ uses only Gaussian operations.​​​‌ In particular, we show​ that with access to​‌ probes of arbitrarily high​​ energy, it is possible​​​‌ to learn the unitary​ with $2m+‌2$ queries at any​​ precision 24.

8.2.4​​​‌ Adaptive Syndrome Extraction Based​ on Heralded Gates

Participants:​‌ Ha Cong Nguyen,​​ Paul Hilaire.

The​​​‌ goal of this project​ is to leverage heralded​‌ errors in fault-tolerant quantum​​ computing to enhance performance.​​​‌ By dynamically reconfiguring quantum​ circuits using classical information​‌ about photonic errors, we​​ exploit these errors more​​​‌ effectively. Our approach is​ applicable to all CSS​‌ codes and has demonstrated​​ a significant improvement in​​​‌ fault-tolerant thresholds. Specifically, it​ achieves over a 20%​‌ increase in the fault-tolerant​​ threshold for the surface​​ code under a circuit-level​​​‌ noise model, while substantially‌ reducing resource requirements. A‌​‌ paper detailing these results​​ is currently in preparation.​​​‌

8.2.5 Comparison of Fusion-Based‌ and Spin-Optical Quantum Computing‌​‌ Architectures Under Photonic Error​​ Models

Participants: Katia Hakem​​​‌, Stephen Wein,‌ Paul Hilaire.

The‌​‌ objective of this project​​ is to compare the​​​‌ efficiency of existing photonic‌ fault-tolerant architectures and photonic‌​‌ sources in terms of​​ error correction performance. We​​​‌ have developed a general‌ strategy to address both‌​‌ distinguishability errors and photon​​ loss. This work includes​​​‌ the first comprehensive performance‌ assessment of distinguishability errors‌​‌ in fusion-based quantum computing.​​ Our findings reveal performance​​​‌ differences of up to‌ an order of magnitude,‌​‌ depending on the specific​​ photonic source and architecture​​​‌ used. A paper presenting‌ these results is currently‌​‌ in preparation.

8.3.1‌ Causal models in quantum‌​‌ theory

Participants: Augustin Vanrietvelde​​, Seonghun Jung,​​​‌ Pablo Arrighi, Octave‌ Mestoudjian.

We are‌​‌ investigating the relationship (and​​ in particular the potential​​​‌ equivalence) between the causal‌ structure of quantum dynamics‌​‌ and their compositional structure.​​ In 43, we​​​‌ presented an important proof,‌ showing that this equivalence‌​‌ holds in a general​​ and important case that​​​‌ of one-dimensional quantum cellular‌ automata. This is based‌​‌ on a general theory​​ of partitions of quantum​​​‌ systems, which we concurrently‌ developed.

8.3.2 Quantum reference‌​‌ frames and compositionality

Participants:​​ Augustin Vanrietvelde, Guilhem​​​‌ Doat.

We are‌ investigating quantum reference frames,‌​‌ in which a system's​​ physical quantities are described​​​‌ with respect to those‌ of a reference, potentially‌​‌ superposed, other system. In​​ doat2025, we proposed a​​​‌ clarification and analysis of‌ the conceptual differences between‌​‌ existing frameworks for describing​​ quantum reference frames, and​​​‌ proposed an operational argument‌ discriminating between these approaches.‌​‌ We are currently working​​ on an analysis and​​​‌ resolution of the paradox‌ of the third particle,‌​‌ a problem arising in​​ the context of these​​​‌ approaches.

8.3.3 Learning complex‌ quantum states

Participants: Marco‌​‌ Fanizza, Cambyse Rouzé​​, Daniel Stilck França​​​‌, James D Watson‌, Tim Möbus,‌​‌ Andreas Bluhm, Matthia​​ C Caro, Giacomo​​​‌ De Palma, Connor‌ Mowry, Ryan O'Donnell‌​‌.

In 67,​​ we initiated the problem​​​‌ of learning the time-dependent‌ evolution of a locally‌​‌ interacting n-qubit system on​​ a graph of effective​​​‌ dimension D using only‌ preparation of product Pauli‌​‌ eigenstates, evolution under the​​ time-dependent generator for given​​​‌ times, and measurements in‌ product Pauli bases. These‌​‌ results provide a scalable​​ tool to verify state-preparation​​​‌ procedures (e.g. adiabatic protocols)‌ and characterize time-dependent noise‌​‌ in quantum devices. In​​ 36 we have considered​​​‌ the problem of testing‌ if the average of‌​‌ an unknown non-iid product​​ state is equal or​​​‌ far from a a‌ target known state, showing‌​‌ that the same performance​​ of the iid case​​​‌ is attainable, also improving‌ analogous results in the‌​‌ classical case. In our​​ analysis, we introduce a​​​‌ quantum generalization of the‌ Efron-Stein inequality.

8.3.4 Complexity‌​‌ of quantum Gibbs states​​​‌

Participants: Ivan Bardet,​ Ángela Capel, Li​‌ Gao, Daniel Stilck​​ França, Angelo Lucia​​​‌, David Peres-García,​ Cambyse Rouzé, Jan​‌ Kochanowski, Alvaro Alhambra​​, Paul Gondolf,​​​‌ Simone Warzel, Sebastian​ Stengele.

We have​‌ kept on working on​​ the complexity of Gibbs​​​‌ sampling algorithms. In 84​, 83, we​‌ proved the first general​​ polynomial runtime bounds for​​​‌ such Gibbs samplers at​ high enough temperature. Our​‌ methods were recently extended​​ to Fermionic Hamiltonians at​​​‌ any temperature, including temperatures​ at which the Gibbs​‌ states are entangled and​​ where no concurrent classical​​​‌ method is currently known​ for the task of​‌ approximating physical properties. In​​ 61, we prove​​​‌ limitations of these algorithms​ by finding a randomized​‌ classical algorithm to compute​​ the log-partition function of​​​‌ weakly interacting fermions with​ polynomial runtime in both​‌ the system size and​​ precision.

Next, we will​​​‌ further investigate the connections​ between sampling and computing​‌ physical properties of quantum​​ many-body systems at thermal​​​‌ equilibrium. More precisely, we​ will focus on proving​‌ lower bounds on known​​ classical algorithms for the​​​‌ latter in parameter ranges​ for which our samplers​‌ converge in polynomial time.​​ We will also study​​​‌ encodings of specific quantum​ algorithms into Gibbs samplers​‌ with the goal of​​ finding better robustness of​​​‌ the latter against standard​ noise models. Extensions to​‌ infinite dimensional systems such​​ as quantum continuous variables​​​‌ will also be considered.​

8.3.5 Development of a​‌ Quantum Error Correction Simulation​​ Framework

Participants: Maxime Garnier​​​‌, Paul Hilaire.​

This project aims to​‌ develop advanced simulation tools​​ for quantum error correction.​​​‌ The framework is designed​ to handle fault-tolerant gates​‌ and adaptive fault-tolerant circuits,​​ such as those used​​​‌ in the adaptive syndrome​ extraction project. It is​‌ continuously evolving to accommodate​​ further developments and offers​​​‌ versatility for a wide​ range of applications in​‌ quantum error correction research.​​ It will be publicly​​​‌ released soon.

8.3.6 Adaptations​ of quantum theory and​‌ how to distinguish them​​ experimentally

Participants: Mirjam Weilenmann​​​‌, Nicolas Gisin,​ Pavel Sekatski, Kuntal​‌ Sengupta, Roger Colbeck​​.

Generalised probabilistic theories​​​‌ are a way to​ understand quantum theory and​‌ its properties in a​​ more general formalism and​​​‌ to understand how deviations​ from it affect the​‌ physical observations we make.​​ We have performed works​​​‌ on comparing quantum theory​ to other such theories,​‌ most notably quantum theory​​ over real Hilbert spaces​​​‌ 13, where we​ showed a difference between​‌ this theory and its​​ complex analogue even under​​​‌ restricted source-independence, refining the​ result from 82.​‌ Our work further proposes​​ a hierarchy of semi​​​‌ definite programs that include​ a partial source independence​‌ contraint, which may be​​ of independent interest.

In​​​‌ addition, we have compared​ the correlations obtainable from​‌ quantum systems with those​​ from another family of​​​‌ theories that lack a​ specific relabelling symmetry 39​‌. We proved that​​ quantum theory outperforms these​​​‌ theories in network experiments.​

8.3.7 Random purification of​‌ states and channels and​​ applications

Participants: Marco Fanizza​​, Senrui Chen,​​​‌ Filippo Girardi, Ludovico‌ Lami, Francesco A.‌​‌ Mele, Haimeng Zhao​​.

The result of​​​‌ 80 greatly simplified the‌ analysis of optimal tomography‌​‌ by deriving a channel​​ that converts copies of​​​‌ a mixed state into‌ copies of the same‌​‌ random purification. We are​​ are exploring extensions of​​​‌ this idea in bosonic‌ systems, where we derived‌​‌ a random purification channel​​ for passive Gaussian states​​​‌ 33, and for‌ channels, were we introduced‌​‌ a random Stinespring dilation​​ supermap for parallel queries,​​​‌ giving an explicit efficient‌ circuit to implement it‌​‌ 28. We are​​ currently working on extending​​​‌ the Gaussian purification to‌ general Gaussian state and‌​‌ the channel dilation to​​ the adaptive setting.

Orange Innovation‌

CIFRE with Orange Innovation‌​‌ (Chatillon) on Discrete Variable​​ Quantum Key Distribution and​​​‌ Time Multiplexing, PhD Student:‌ Pierre-Enguerrand Verdier.

Paris Region​​ PhD Grant, collaboration with​​​‌ Quandela

Doctoral project of‌ Guillaume Ricard, on Quatum‌​‌ Coherent Communications and Digital​​ Signal Processing, Funded by​​​‌ Paris funded by Paris‌ Region (region Ile-de France)‌​‌ in the context of​​ the Paris Region PhD​​​‌ call, with a planned‌ collaboration with Quandela on‌​‌ noise mitigation in optical​​ coherent quantum communications.

CIFRE​​​‌ PhD Grant, collaboration with‌ Quandela

Doctoral project of‌​‌ Katia Hakem, on fault-tolerant​​ quantum computation with photonic​​​‌ hardware-constraints model, funded by‌ ANRT.

10.1.1 Visits of​​​‌ international scientists

Artymowicz Adam‌

• Status
  PhD
• Institution of‌​‌ origin
  Caltech
• Country
  USA​​
• Dates
  3rd February -​​​‌ 7th February
• Context of‌ visit
  Visiting Cambyse Rouzé‌​‌
• Type of mobility
  Research​​ visit, talk

Zaw Lin​​​‌ Htoo

• Status
  PhD
• Institution‌ of origin
  Singapore Centre‌​‌ for Quantum Technologies
• Country​​
  Singapore
• Dates
  7th April​​​‌ - 11th April
• Context‌ of visit
  Visiting Mirjam‌​‌ Weilenmann
• Type of mobility​​
  Research visit, talk

Scalet​​​‌ Samuel

• Status
  PhD
• Institution‌ of origin
  University of‌​‌ Cambridge
• Country
  UK
• Dates​​
  February - April
• Context​​​‌ of visit
  Visiting Cambyse‌ Rouzé
• Type of mobility‌​‌
  Research visit, talk

Budroni​​ Constantino

• Status
  Professor
• Institution​​​‌ of origin
  University of‌ Pisa
• Country
  Italy
• Dates‌​‌
  2nd June - 6th​​ June
• Context of visit​​​‌
  Visiting Mirjam Weilenmann
• Type‌ of mobility
  Research visit,‌​‌ talk

Navascues Miguel

• Status​​
  Research Group Leader
• Institution​​​‌ of origin
  IQOQI Vienna‌
• Country
  Austria
• Dates
  2nd‌​‌ June - 6th June​​
• Context of visit
  Visiting​​​‌ Mirjam Weilenmann
• Type of‌ mobility
  Research visit, talk‌​‌

Lumbreras Josep

• Status
  PhD​​
• Institution of origin
  National​​​‌ University of Singapore
• Country‌
  Singapore
• Dates
  2nd September‌​‌
• Context of visit
  Seminar​​ Talk
• Type of mobility​​​‌
  Research visit, talk

Hahn‌ Thomas

• Status
  PhD
• Institution‌​‌ of origin
  Weizmann Institute​​
• Country
  Israel
• Dates
  10th​​​‌ November - 14th November‌
• Context of visit
  Visiting‌​‌ Jan Kochanowski
• Type of​​ mobility
  Research visit, talk​​​‌

Angrisani Armando

• Status
  Postdoc‌
• Institution of origin
  EPFL‌​‌ Lausanne
• Country
  Switzerland
• Dates​​
  1st December - 5th​​​‌ December
• Context of visit‌
  Visiting team
• Type of‌​‌ mobility
  Research visit, talk​​​‌

Ulu Bora

• Status
  PhD​
• Institution of origin
  University​‌ of Geneva
• Country
  Switzerland​​
• Dates
  November - December​​​‌
• Context of visit
  Visiting​ Mirjam Weilenmann
• Type of​‌ mobility
  Research visit, talk​​

10.2.1​​​‌ Horizon Europe

10.2.2 Digital Europe​​

PEPR QCommTestbed​​​‌

Participants: Romain Alléaume,‌ Peter Brown, Nicolas‌​‌ Fabre, Yves Jaouën​​, Tristan Nemoz,​​​‌ Thomas Pousset.

• Partner‌ Institutions:
  1. Institut-Mines-Telecom (IMT), France‌​‌
  2. CNRS Université Cote d'Azur,​​ France
  3. Sorbonne Université, France​​​‌
  4. CEA Leti, France
  5. C2N,‌ France
  6. Université Paris-Cité, France‌​‌
• Contract ID:
  PC 4.3​​ « QCommTestbed » (Quantum​​​‌ communication testbeds)
• Duration:
  01/07/2022‌ – 30/06/2027
• Description:
  The‌​‌ objective of the QcommTestbed​​ project is to lay​​​‌ the foundations for fiber‌ optic and free-space quantum‌​‌ networks on a regional​​ and longer-term national scale,​​​‌ making it possible to‌ connect systems including quantum‌​‌ elements (transmitters and receivers,​​ processors, sensors) via repeater​​​‌ nodes. The project also‌ aims to make decisive‌​‌ advances in the TRL​​ of quantum communication systems,​​​‌ and also in their‌ security evaluation and testing,‌​‌ to pave the way​​​‌ for their wider adoption​ and ubiquituous deployment.
• Role​‌ of Quriosity:
  • Demonstration​​ of ITS secure communication​​​‌ over a single fiber,​ based on joint CV-QKD​‌ and classical communication integration.​​
  • Performance and Cost of​​​‌ Long-Term Secure Storage based​ on CV-QKD
  • Vulnerability analysis​‌ of a QKD (VAN)​​ system. Definition of an​​​‌ evaluation methodology (based on​ the Common Criteria.
  • Experimental​‌ Demonstration of Mulimode Frequency-encoded​​ Key Distribution in the​​​‌ QCT model

HQI –​ Hybrid Quantum Initiative

Participants:​‌ Cambyse Rouzé, Paul​​ Hilaire.

• Partner Institutions:​​​‌
  1. Inria, France
  2. CNRS, France​
  3. CEA, France
• Contract ID:​‌
  ANR-22- PNCQ-0002
• Duration:
  2023​​ – 2028
• Description:
  the​​​‌ HQI iniative aims at​ developing a hybrid computing​‌ platform, interconnecting classical HPC​​ systems with quantum devices,​​​‌ seen as accelerators. It​ will be available for​‌ an international community bringing​​ together laboratories, start-ups and​​​‌ industries. The goal is​ to make it easier​‌ for them to access​​ quantum computing, to identify,​​​‌ develop and test new​ use case. The research​‌ program is led by​​ CEA and Inria, supported​​​‌ by GENCI and France​ Universités. Endowed with a​‌ €36M budget, it aims​​ at developing a programming​​​‌ and compilation software stack​ for hybrid computing, including​‌ libraries for specific business​​ (healthcare, chemistry, finance, etc)​​​‌ or transversal (Machine Learning,​ optimization, etc) applications.
• Role​‌ of Quriosity:
  • Coordination​​ of Work Package 5​​​‌ on characterization and correction​ of noise in hybrid​‌ quantum systems.
  • Development of​​ theoretical and experimental methodologies​​​‌ for noise identification, modeling,​ and mitigation in quantum​‌ communication and hybrid quantum​​ platforms.
  • Contribution to cross-platform​​​‌ benchmarking and validation protocols.​
  • Design and integration of​‌ a library of early​​ fault-tolerant quantum error-correcting codes​​​‌ adapted to noisy intermediate-scale​ and hybrid quantum architectures.​‌

11.1.1 Scientific​​​‌ events: organisation

11.1.2 Scientific events: selection​​

11.1.3 Journal

11.1.4 Invited​​ talks

• Peter Brown. Invited​​​‌ Tutorial at Mathematical Aspects​ of Quantum Information Summer​‌ School, Paris-Saclay. Title: Randomness,​​ entropy and accumulation.
• Peter​​​‌ Brown. Invited Tutorial at​ Young Quantum Information Scientists​‌ Conference, Barcelona. Title: Device-independent​​ cryptography.
• Mirjam Weilenmann: Invited​​ tutorial at the Mathematics​​​‌ and Physics of Quantum‌ Computing and Quantum Learning,‌​‌ Porquerolles. Title: Quantum Correlations.​​
• Mirjam Weilenmann: Invited tutorial​​​‌ at the Mathematical Aspects‌ of Quantum Information summer‌​‌ school, Institut Pascal, Université​​ Paris Saclay. Title: Network​​​‌ non-locality.
• Mirjam Weilenmann: Invited‌ talk at 15th annual‌​‌ conference on relativistic quantum​​ information (north), Naples, June​​​‌ 2025. Title: Monogamy relations‌ for relativistically causal correlations.‌​‌
• Cambyse Rouzé: Invited tutorial​​ at QIP 2025, Raleigh,​​​‌ February 2025. Title: Quantum‌ Gibbs sampling.
• Augustin Vanrietvelde:‌​‌ Invited talk at QISS​​ 2025, Vienna, Qpril 2025.​​​‌ Title: Fighting for a‌ cause.
• Marco Fanizza: Invited‌​‌ tutorial at 1st AIMS​​ Workshop and School on​​​‌ The Theory of Quantum‌ Learning Algorithms, AIMS, Cape‌​‌ Town, South Africa, Nov​​ 2025. Title: Tutorial on​​​‌ Quantum state certification and‌ quantum tomography.
• Marco Fanizza:‌​‌ Invited talk 6th Nottingham​​ Workshop on Quantum Non-Equilibrium​​​‌ Dynamics, University of Nottingham,‌ UK, Oct 2025. Title:‌​‌ Modelling and learning finitely​​ correlated states.
• Romain Alléaume:​​​‌ Invited talk at the‌ Workshop on Entanglement Assisted‌​‌ Communication Networks (EACN), September​​ 10 to 12 at​​​‌ EURECOM, Sophia Antipolis. Title:‌ Quantum cryptography from decoherence‌​‌ and short-term computational assumptions​​ .

11.1.5 Leadership within​​​‌ the scienific community

• Romain‌ Alléaume as member of‌​‌ the ANR CE47 committee​​ on Quantum Technologies
• Romain​​​‌ Alléaume as member of‌ QSNP Executive board
• Romain‌​‌ Alléaume as member of​​ the QuantiP bureau, for​​​‌ the Quantum Communication axis.‌
• Romain Alléaume as Rapporteur,‌​‌ for the Quantum PEPR​​ scientific workshop (Cryptography and​​​‌ Quantum Networks).

11.1.6 Scientific‌ expertise

• Peter Brown as‌​‌ grant reviewer
• Augustin Vanrietvelde​​ as reviewer for various​​​‌ grants
• Romain Alléaume as‌ grant reviewer

11.1.7 Research‌​‌ administration

• Peter Brown as​​ member of the LTCI​​​‌ council.
• Peter Brown as‌ référent mobilité.
• Romain Alléaume‌​‌ as member for the​​ Quantum-Saclay Comex.
• Romain Alléaume​​​‌ as member of the‌ Step2 steering committee.
• Romain‌​‌ Alléaume as member of​​ the conseil du LTCI.​​​‌
• Romain Alléaume as member‌ of the PhD Track‌​‌ Quantum Science and Technology​​ committee.

11.2.1 Teaching

11.2.2 Supervision​​​‌

11.2.3 Juries

International journals‌​‌

• 5 articleR.Romain​​ Alléaume and T.Tristan​​​‌ Nemoz. Approches hybrides‌ en cryptographie quantique.‌​‌Photoniques130March 2025​​, 46-48HALDOI​​​‌back to text
• 6‌ articleD.Dmitri Horoshko‌​‌, S.Shivang Srivastava​​, F.Filip Sośnicki​​​‌, M.Michał Mikołajczyk‌, M.Michał Karpiński‌​‌, B.Benjamin Brecht​​ and M.Mikhail Kolobov​​​‌. Time-resolved second-order autocorrelation‌ function of parametric down-conversion‌​‌.Physical Review A​​1122August 2025​​​‌, 023703-1:023703-13HALDOI‌
• 7 articleJ.Jan‌​‌ Kochanowski, Á.Álvaro​​ Alhambra, Á.Ángela​​​‌ Capel and C.Cambyse‌ Rouzé. Rapid Thermalization‌​‌ of Dissipative Many-Body Dynamics​​ of Commuting Hamiltonians.​​​‌Communications in Mathematical Physics‌4068July 2025‌​‌, 176HALDOI​​
• 8 articleF.Francesco​​​‌ Mazzoncini, B.Balthazar‌ Bauer, P.Peter‌​‌ Brown and R.Romain​​ Alléaume. Hybrid Quantum​​​‌ Cryptography from Communication Complexity‌.Quantum9September‌​‌ 2025, 1862HAL​​DOIback to text​​​‌
• 9 articleT.Thomas‌ Pousset, M.Maxime‌​‌ Federico, R.Romain​​ Alléaume and N.Nicolas​​​‌ Fabre. Kramers-Kronig detection‌ in the quantum regime‌​‌.Physical Review Research​​74December 2025​​​‌, 043287HALDOI‌back to text
• 10‌​‌ articleB.Bora Ulu​​, N.Nicolas Brunner​​​‌ and M.Mirjam Weilenmann‌. Device Independent Quantum‌​‌ Key Activation.Physical​​ Review Letters13519​​​‌2025, 190801HAL‌DOIback to text‌​‌
• 11 articleP.-E.Pierre-Enguerrand​​ Verdier, R.Romain​​​‌ Alléaume and T.Thomas‌ Rivera. Investigating Raman‌​‌ backscattering decay and the​​ perspective of time-multiplexed quantum​​​‌ communications.Optics Express‌3315July 2025‌​‌, 31029-31041HALDOI​​back to text
• 12​​​‌ articleM.Mirjam Weilenmann‌, C.Costantino Budroni‌​‌ and M.Miguel Navascués​​. Memory attacks in​​​‌ network nonlocality and self-testing‌.Quantum9May‌​‌ 2025, 1735HAL​​DOIback to text​​​‌
• 13 articleM.Mirjam‌ Weilenmann, N.Nicolas‌​‌ Gisin and P.Pavel​​ Sekatski. Partial Independence​​​‌ Suffices to Rule Out‌ Real Quantum Theory Experimentally‌​‌.Physical Review Letters​​13518October 2025​​​‌, 180201HALDOI‌back to text
• 14‌​‌ articleL.Lewis Wooltorton​​, P.Peter Brown​​​‌ and R.Roger Colbeck‌. Expanding bipartite Bell‌​‌ inequalities for maximum multi-partite​​​‌ randomness.Quantum9​December 2025, 1930​‌HALDOIback to​​ text
• 15 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 Letters135​​22November 2025,​​​‌ 220803HALDOIback​ to text
• 16 article​‌W.-B.Wen-Bo Xing,​​ M.-Y.Min-Yu Lv,​​​‌ L.Lingxia Zhang,​ Y.Yu Guo,​‌ M.Mirjam Weilenmann,​​ Z.Zhaohui Wei,​​​‌ C.-F.Chuan-Feng Li,​ G.-C.Guang-Can Guo,​‌ X.-M.Xiao-Min Hu,​​ B.-H.Bi-Heng Liu,​​​‌ M.Miguel Navascués and​ Z.Zizhu Wang.​‌ Practical Advantage of Classical​​ Communication in Entanglement Detection​​​‌.Physical Review Letters​13513September 2025​‌, 130805HALDOI​​

International peer-reviewed conferences

• 17​​​‌ 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 ComputingPrague Czechia,​ Czech RepublicACMJune​‌ 2025, 1488-1495HAL​​DOI

Conferences without proceedings​​​‌

• 18 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, India2025​​HAL

Reports & preprints​​​‌

• 19 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
• 20 miscH.​Hongrui Chen, C.​‌Cambyse Rouzé, J.​​Jielun Chen, J.​​​‌Jiaqing Jiang, S.​Samuel Scalet, Y.​‌Yongtao Zhan, G.-L.​​ K.Garnet Kin-Lic Chan​​​‌, L.Lexing Ying​ and Y.Yu Tong​‌. Convergence of the​​ Cumulant Expansion and Polynomial-Time​​​‌ Algorithm for Weakly Interacting​ Fermions.2025HAL​‌DOI
• 21 miscC.-F.​​Chi-Fang Chen and C.​​​‌Cambyse Rouzé. Quantum​ Gibbs states are locally​‌ Markovian.2025HAL​​
• 22 miscI.Idris​​​‌ Delsol, O.Omar​ Fawzi, J.Jan​‌ Kochanowski and A.Akshay​​ Ramachandran. Computational aspects​​​‌ of the trace norm​ contraction coefficient.2025​‌HAL
• 23 miscG.​​Guilhem Doat and A.​​​‌Augustin Vanrietvelde. What​ can we do in​‌ a symmetry-constrained perspective? The​​ importance of the total​​​‌ charge's status in quantum​ reference frame frameworks.​‌October 2025HAL
• 24​​ miscM.Marco Fanizza​​​‌, V.Vishnu Iyer​, J.Junseo Lee​‌, A. A.Antonio​​ A. Mele and F.​​​‌ A.Francesco A. Mele​. Efficient learning of​‌ bosonic Gaussian unitaries.​​October 2025HALDOI​​​‌back to text
• 25​ miscM.Marco Fanizza​‌, L.Larissa Kroell​​, A.Arthur Mehta​​​‌, C.Connor Paddock​, D.Denis Rochette​‌, W.William Slofstra​​ and Y.Yuming Zhao​​. The NPA hierarchy​​​‌ does not always attain‌ the commuting operator value‌​‌.2025HALDOI​​
• 26 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.2025​​HAL
• 27 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.​​2025HAL
• 28 misc​​​‌F.Filippo Girardi,‌ F. A.Francesco Anna‌​‌ Mele, H.Haimeng​​ Zhao, M.Marco​​​‌ Fanizza and L.Ludovico‌ Lami. Random Stinespring‌​‌ superchannel: converting channel queries​​ into dilation isometry queries​​​‌.2025HALback‌ to text
• 29 misc‌​‌M.Maarten Grothus,​​ A. A.Alastair A.​​​‌ Abbott, A.Augustin‌ Vanrietvelde and C.Cyril‌​‌ Branciard. Routing Quantum​​ Control of Causal Order​​​‌.2025HAL
• 30‌ miscT.Thomas Hahn‌​‌, A.Aby Philip​​, E.Ernest Tan​​​‌ and P.Peter Brown‌. Analytic Rényi Entropy‌​‌ Bounds for Device-Independent Cryptography​​.2025HALDOI​​​‌back to text
• 31‌ miscJ.Jan Kochanowski‌​‌, O.Omar Fawzi​​ and C.Cambyse Rouzé​​​‌. Complexity of mixed‌ Schatten norms of quantum‌​‌ maps.2025HAL​​
• 32 miscK.Konstantinos​​​‌ Manos, M.Mirjam‌ Weilenmann and M.Miguel‌​‌ Navascués. Extrapolation of​​ quantum measurement data.​​​‌2025HAL
• 33 misc‌F. A.Francesco Anna‌​‌ Mele, F.Filippo​​ Girardi, S.Senrui​​​‌ Chen, M.Marco‌ Fanizza and L.Ludovico‌​‌ Lami. Random purification​​ channel for passive Gaussian​​​‌ bosons.December 2025‌HALDOIback to‌​‌ text
• 34 miscT.​​Tim Möbus, A.​​​‌Andreas Bluhm, T.‌Tuvia Gefen, Y.‌​‌Yu Tong, A.​​Albert Werner and C.​​​‌Cambyse Rouzé. Heisenberg-limited‌ Hamiltonian learning continuous variable‌​‌ systems via engineered dissipation​​.2025HAL
• 35​​​‌ miscT.Tristan Nemoz‌, R.Romain Alléaume‌​‌ and P.Peter Brown​​. Exact distinguishability between​​​‌ real-valued and complex-valued Haar‌ random quantum states.‌​‌2025HALback to​​ text
• 36 miscG.​​​‌Giacomo de Palma,‌ M.Marco Fanizza,‌​‌ C.Connor Mowry and​​ R.Ryan O'Donnell.​​​‌ Non-iid hypothesis testing: from‌ classical to quantum.‌​‌2025HALDOIback​​ to text
• 37 misc​​​‌Y.Yoann Piétri,‌ P.-E.Pierre-Enguerrand Verdier,‌​‌ B.Baptiste Lacour,​​ M.Maxime Gautier,​​​‌ H.Heming Huang,‌ T.Thomas Camus,‌​‌ J.-S.Jean-Sébastien Pegon,​​ M.Martin Zuber,​​​‌ J.-C.Jean-Charles Faugère,‌ M.Matteo Schiavon,‌​‌ A.Amine Rhouni,​​ Y.Yves Jaouën,​​​‌ N.Nicolas Fabre,‌ R.Romain Alléaume,‌​‌ T.Thomas Rivera and​​ E.Eleni Diamanti.​​​‌ Quantum Key Distribution with‌ Efficient Post-Quantum Cryptography-Secured Trusted‌​‌ Node on a Quantum​​ Network.April 2025​​​‌HALDOI
• 38 misc‌G.Guillaume Ricard,‌​‌ Y.Yves Jaouën and​​ R.Romain Alléaume.​​​‌ Receiver Noise Calibration in‌ CV-QKD accounting for Noise‌​‌ Dynamics.2025,​​​‌ 043287HALDOIback​ to text
• 39 misc​‌K.Kuntal Sengupta,​​ M.Mirjam Weilenmann and​​​‌ R.Roger Colbeck.​ Correlation Self-Testing of Quantum​‌ Theory against Generalised Probabilistic​​ Theories with Restricted Relabelling​​​‌ Symmetry.2025HAL​back to text
• 40​‌ miscS.Sebastian Stengele​​, Á.Ángela Capel​​​‌, L.Li Gao​, A.Angelo Lucia​‌, D.David Pérez-García​​, A.Antonio Pérez-Hernández​​​‌, C.Cambyse Rouzé​ and S.Simone Warzel​‌. Modified logarithmic Sobolev​​ inequalities for CSS codes​​​‌.2025HAL
• 41​ miscV.Vladyslav Usenko​‌, A.Antonio Acín​​, R.Romain Alléaume​​​‌, U.Ulrik Andersen​, E.Eleni Diamanti​‌, T.Tobias Gehring​​, A.Adnan Hajomer​​​‌, F.Florian Kanitschar​, C.Christoph Pacher​‌, S.Stefano Pirandola​​ and V.Valerio Pruneri​​​‌. Continuous-variable quantum communication​.2025HALDOI​‌back to text
• 42​​ miscA.Augustin Vanrietvelde​​​‌, O.Octave Mestoudjian​ and P.Pablo Arrighi​‌. Causal decompositions of​​ one-dimensional quantum cellular automata​​​‌.September 2025HAL​
• 43 miscA.Augustin​‌ Vanrietvelde, O.Octave​​ Mestoudjian and P.Pablo​​​‌ Arrighi. Partitions in​ quantum theory.September​‌ 2025HALback to​​ text
• 44 miscÁ.​​​‌Álvaro Yángüez, T.​ A.Thomas A Hahn​‌ and J.Jan Kochanowski​​. Efficient Quantum Measurements:​​​‌ Computational Max-and Measured Rényi​ Divergences and Applications.​‌September 2025HAL

Other​​ scientific publications

• 45 article​​​‌P.Peter Brown.​ Cheat-proof random numbers generated​‌ from quantum entanglement.​​Nature6428069June​​​‌ 2025, 875-876HAL​DOI