On the volume of the set of mixed entangled states

1998/04/09 by Karol Zyczkowski, Pawel Horodecki, Anna Sanpera +1 · 5 citations
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1103/physreva.58.883

published as Phys.Rev. A58 (1998) 883 · 10 pages in LaTex - RevTex + 4 figures in eps. submitted to Phys. Rev. A

arxiv created 1998/04/09 · arxiv updated 2009/12/01

Abstract

A natural measure in the space of density matrices describing N-dimensional quantum systems is proposed. We study the probability P that a quantum state chosen randomly with respect to the natural measure is not entangled (is separable). We find analytical lower and upper bounds for this quantity. Numerical calculations give P = 0.632 for N=4 and P=0.384 for N=6, and indicate that P decreases exponentially with N. Analysis of a conditional measure of separability under the condition of fixed purity shows a clear dualism between purity and separability: entanglement is typical for pure states, while separability is connected with quantum mixtures. In particular, states of sufficiently low purity are necessarily separable.

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