Section: New Results

Quantum information theory

Participants : André Chailloux, Anthony Leverrier, Denise Maurice, Jean-Pierre Tillich.

The field of Quantum Information and Computation aims at exploiting the laws of quantum physics to manipulate information in radically novel ways. Two main applications come to mind: quantum computers, that offer the promise of solving some problems intractable with classical computers (for instance, factorization); and quantum cryptography, which provides new ways to exchange data in a provably secure fashion.

The main obstacle towards the development of quantum computing is decoherence, a consequence of the interaction of the computer with a noisy environment. We investigate approaches to quantum error-correction as a way to fight against this effect, and we study more particularly some families of quantum error-correcting codes which generalise the best classical codes available today.

Our research also covers quantum cryptography where we study the security of efficient protocols for key distribution, in collaboration with experimental groups. More generally, we investigate how quantum theory severely constrains the action of honest and malicious parties in cryptographic scenarios.

Quantum codes

Protecting quantum information from external noise is an issue of paramount importance for building a quantum computer. It also worthwhile to notice that all quantum error-correcting code schemes proposed up to now suffer from the very same problem that the first (classical) error-correcting codes had: there are constructions of good quantum codes, but for the best of them it is not known how to decode them in polynomial time. Our approach for overcoming this problem has been to study whether or not the family of turbo-codes and LDPC codes (and the associated iterative decoding algorithms) have a quantum counterpart.

Recent results:

• Construction of quantum codes combining an improved version of a family of spatially coupled quantum LDPC codes with a family of error reducing turbo-codes [44] ;

• construction of quantum LDPC codes with fixed non-zero rate and a minimum distance which grows proportionally to the square root of the block-length. This greatly improves the previously best known construction whose minimum distance was logarithmic in the block-length [19] .

• Mamdouh Abbara's PhD thesis [9]

Quantum cryptography

A recent approach to cryptography takes into account that all interactions occur in a physical world described by the laws of quantum physics. These laws put severe constraints on what an adversary can achieve, and allow for instance to design provably secure key distribution protocols. We study such protocols as well as more general cryptographic primitives with security properties based on quantum theory.

Recent results:

• Experimental demonstration of quantum key distribution with continuous variables over 80 km [15] , greatly improving over previous records around 25 km.

• Security proof of continuous-variable quantum key distribution protocols against general attacks [17] , [29] .

• Security proof of device-independent quantum key distribution in the bounded storage model [18] .

• Study of BosonSampling, a recently introduced problem where quantum computers offer a provable speedup over classical computers [67] , [28] .

• Introduction and study of “Local Orthogonality”, an information-theoretical principle for quantum correlations [13] , [68] .

• Introduction of a general formalism for the study of contextuality and non locality in quantum theory, based on the combinatorics of hypergraphs [65] , [27] .