Lyon, 8-9 October 2012

The first workshop of the ANR OSQPI (Operator Spaces, Quantum Probability and Information) will take place in Lyon (Institut Camille Jordan), 8-9 October 2012.

The topics of the workshop are: Operator spaces, Non-commutative L^p spaces, Non-commutative probability and applications to Quantum Information Theory (entanglement, Bell inequalities).


Monday, October 8th :

Tuesday, October 9th :

Speakers and titles

Cédric Arhancet. Square functions for Ritt operators on noncommutative $L^p$-spaces

arxiv preprint

Steve Avsec. A Characterization of Noncommutative Brownian Motion

We prove an equivalence between a class of noncommutative Brownian motions and real-valued positive definite functions on the infinite symmetric group with a certain invariance property. This invariance property ensures that the Brownian motion is affiliated to a Type II_1 von Neumann algebra. In certain cases we are able to establish the weak* CBAP and strong solidity for these von Neumann algebras. This is joint work with Marius Junge.

Jean-Christophe Bourin. Unitary Orbits and Decompositions of Positive Matrices

A unitary orbit technique is useful to prove some matrix inequalities. This also yields interesting decompositions of partitioned positive matrices. These decomposition are related to majorisations in quantum information theory such as the Nielsen-Kempe separability criterion.

Martijn Caspers. The best constants for operator Lipschitz functions on Schatten classes

Abstract: It was proved by D. Potapov and F. Sukochev that a Lipschitz function f on the reals satisfies an operator Lipschitz inequality in Schatten classes S_p for 1 < p < infinity. That is, if A and B are in S_p, then f(A) - f(B) will be in S_p and its norm can be estimated by a constant C_p times the norm of A-B. This statement is known to be false in the cases p=1 and p=infinity. Our main result is a sharp bound for the asymptotic behavior of C_p as p approaches either 1 or infinity. The talk is based on a joint work with S. Montgomery-Smith, D. Potapov, F. Sukochev.

Uwe Franz. On the quantum symmetry group of a complex Hadamard matrix

Abstract: To each complex Hadamard matrix one can associate a unique "quantum symmetry group" (or quantum permutation group, i.e. a subgroup of the free permutation compact quantum group $S_N^+$). Many questions about the subfactors and planar algebras associated to a Hadamard matrix have an equivalent formulations in terms of its quantum symmetry group. In my talk I will present a probabilistic approach to characterising this quantum symmetry group and study several examples in small dimension. Based on joint work with Teodor Banica and Adam Skalski

Guixiang Hong. Behavior of the bounds of operator-valued maximal inequality in R^n for large n

In this talk, I will talk about a generalization of Stein and Stromberg's results on behavior of scalar-valued maximal functions. More precisely, we prove that the Lp-bounds (p>1) of operator-valued maximal inequality in R^n can be taken to be independent of n

Chunlan Jiang. On generalized universal irrational rotation algebras

We introduce a class of generalized universal irrational rotation C^*-algebras and characerize its tracial linear functionals, simplicity and K-groups.We also show that if the algebra is simple, then it is an $AT$-algebra of real rank zero.

Cécilia Lancien. Distinguishing multi-partite states by local measurements

arxiv preprint

Władysław A. Majewski. On entanglement, quantum correlations, and positive maps.

In our talk we present the notion of coefficient of quantum correlations. This concept stems from the rigorous description of entanglement of formation. In particular, using a characterization of the structure of positive maps, it will be shown that vanishing coefficient of quantum correlations implies the separability of a state. All will be done within the $C^*$-algebraic approach to the theory of quantum systems. In particular, the characterization of entanglement is based on the applications of the theory of compact sets and boundary integrals to decompositions of states of $C^*$-algebras.

Ion Nechita. Positive and completely positive maps via free additive powers of probability measures

We give examples of maps between matrix algebras with different"degrees of positivity" using ideas from free probability. We discuss applications to Quantum Information Theory.

Stefan Neuwirth. Some peculiar Schur multipliers

Mathilde Perrin. Hypercontractivity for free products

After a brief historical introduction to the wide subject of Hypercontractivity and its closed relation with the Logarithmic Sobolev inequalities, this talk will focus on hypercontractivity for free products. We will first consider the noncommutative analogue of Nelson’s inequalities in the Gaussian case, and following Biane’s probabilistic approach we study the hypercontractivity of the free product of Ornstein-Uhlenbeck semigroups on Clifford algebras. The second part of the talk will deal with a free product version of the Bonami-Beckner Theorem. We will discuss the hypercontractivity of the free Poisson semigroup on the group von Neumann algebras generated by Z2 ∗ · · · ∗ Z2 and Fn = Z ∗ · · · ∗ Z respectively, by using two complementary methods: a probabilistic approach and a combinatorial one.

Gilles Pisier. Quantum Expanders, Random matrices and Geometry of Operator Spaces

arxiv preprint

Quanhua Xu. Atomic decomposition of Hardy spaces of noncommutative martingales

We present the atomic decomposition of Hardy spaces $h_p$ of noncommutative martingales. Our proof is contratuctive. A similar approach can be used to give an explicit noncommutative Davis type decomposition.


How to come

To register, or for any question, please contact the organisers:

Guillaume Aubrun (Lyon), Mikael de la Salle (Besançon)