On the volume of the set of mixed entangled states

Details On the volume of the set of mixed entangled states On the volume of the set of mixed entangled states

1998-04-09

arxiv.org/abs/quant-ph/9804024v1

Phys.Rev. A58 (1998) 883

Physics

Quantum Physics

10 pages in LaTex - RevTex + 4 figures in eps. submitted to Phys. Rev. A

Scientific paper

10.1103/PhysRevA.58.883

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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