The purpose of this review is to present some of the latest developments using random
techniques, and in particular, random matrix techniques in quantum information theory. Our …

Entanglement detection is essential in quantum information science and quantum many-
body physics. It has been proved that entanglement exists almost surely for a random …

We study random matrices acting on tensor product spaces which have been transformed by
a linear block operation. Using operator-valued free probability theory, under some mild …

Time is one of the undisputed foundations of our life in the real world. Here it is argued that
inside small isolated quantum systems, time does not pass as we are used to, and it is …

We characterize the boundary of the convex compact set of absolutely separable states,
referred as AS, that cannot be transformed to entangled states by global unitary operators, in …

Entangled states are undoubtedly an integral part of various quantum information
processing tasks. On the other hand, absolutely separable states which cannot be made …

The idea of detecting the entanglement of a given bipartite state by searching for symmetric
extensions of this state was first proposed by Doherty et al. The complete family of …

We study entanglement‐related properties of random quantum states which are unitarily
invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary …

Recent developments have found unexpected connections between non-commutative
probability theory and algebraic topology. In particular, Boolean cumulants functionals seem …

Ce mémoire d'habilitation à diriger des recherches synthétise les activités de recherche que
j'ai effectuées entre 2006 et 2016 en tant que maître de conférences à l'Université Claude …