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arXiv · 1010.1485

How often is a random quantum state k-entangled?

Stanislaw J. Szarek·Elisabeth Werner·Karol Zyczkowski
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Abstract

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,...,d. Working with the measure induced by the Hilbert-Schmidt distance we derive asymptotically tight bounds for the volumes of these sets. Our results strongly suggest that the inner set of (k+1)-positive maps forms a small fraction of the outer set of k-positive maps. These results are related to analogous bounds for the relative volume of the sets of k-entangled states describing a bipartite d X d system.

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Stanislaw J. Szarek, Elisabeth Werner, Karol Zyczkowski. 2010-10-07. How often is a random quantum state k-entangled?. https://doi.org/10.1088/1751-8113/44/4/045303

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