153 citations · 485 across the 45 of their papers we have counts for
7 papers · 1 filter
How often is a random quantum state k-entangled?
Stanislaw J. Szarek, Elisabeth Werner, Karol Zyczkowski
The set of trace preserving, positive maps acting on density matrices of size d forms a convex body. We investigate its nested subsets consisting of k-positive maps, where k=2,...,…
Hastings' additivity counterexample via Dvoretzky's theorem
Guillaume Aubrun, Stanislaw Szarek, Elisabeth Werner
The goal of this note is to show that Hastings' counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky's th…
Non-additivity of Renyi entropy and Dvoretzky's Theorem
Guillaume Aubrun, Stanislaw Szarek, Elisabeth Werner
The goal of this note is to show that the analysis of the minimum output p-Renyi entropy of a typical quantum channel essentially amounts to applying Milman's version of Dvoretzky'…
Bipartite states of low rank are almost surely entangled
Mary Beth Ruskai, Elisabeth M. Werner
We show that a bipartite state on a tensor product of two matrix algebras is almost surely entangled if its rank is not greater than that of one of its reduced density matrices.
Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive
Stanislaw J. Szarek, Elisabeth Werner, Karol Zyczkowski
We investigate the set a) of positive, trace preserving maps acting on density matrices of size N, and a sequence of its nested subsets: the sets of maps which are b) decomposable,…
An Analysis of Completely-Positive Trace-Preserving Maps on 2x2 Matrices
Mary Beth Ruskai, Stanislaw Szarek, Elisabeth Werner
We give a useful new characterization of the set of all completely positive, trace-preserving (i.e., stochastic) maps from 2x2 matrices to 2x2 matrices. These conditions allow one…