On the volume of the set of mixed entangled states
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.
Cite
@article{arxiv.quant-ph/9804024,
title = {On the volume of the set of mixed entangled states},
author = {Karol Zyczkowski and Pawel Horodecki and Anna Sanpera and Maciej Lewenstein},
journal= {arXiv preprint arXiv:quant-ph/9804024},
year = {2009}
}
Comments
10 pages in LaTex - RevTex + 4 figures in eps. submitted to Phys. Rev. A