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Open Quantum Systems Decoherence
Entanglement Theory Quantum Correlations
How often is a random quantum state k-entangled?
arXiv
Authors: Stanislaw J. Szarek, Elisabeth Werner, Karol Zyczkowski
Year
2010
Paper ID
10956
Status
Preprint
Abstract Read
~2 min
Abstract Words
97
Citations
N/A
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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- This paper contributes to the Entanglement Theory & Quantum Correlations research area in the Quantum Articles archive.
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- The set of trace preserving, positive maps acting on density matrices of size d forms a convex body.
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