Non-additivity of Renyi entropy and Dvoretzky's Theorem (2009)
Aubrun, Guillaume, Szarek, Stanislaw, Werner, Elisabeth
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's Theorem about...
On the structure of the body of states with positive partial transpose (2005)
Szarek, Stanislaw, Bengtsson, Ingemar, Zyczkowski, Karol
We show that the convex set of separable mixed states of the 2 x 2 system is a body of constant height. This fact is used to prove that the probability to find a random state to be separable equals 2...
The volume of separable states is super-doubly-exponentially small (2003)
In this note we give sharp estimates on the volume of the set of separable states on N qubits. In particular, the magnitude of the "effective radius" of that set in the sense of volume is determined...
An Analysis of Completely-Positive Trace-Preserving Maps on 2x2 Matrices (2000)
Ruskai, Mary Beth, Szarek, Stanislaw, Werner, Elisabeth
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 to easily check any...