dorsal/arxiv
View SchemaOn the structure of the body of states with positive partial transpose
| Authors | Stanislaw Szarek, Ingemar Bengtsson, Karol Zyczkowski |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0509008 |
| URL | https://arxiv.org/abs/quant-ph/0509008 |
| DOI | 10.1088/0305-4470/39/5/L02 |
| Journal | J. Phys. A 39 L119-L126 (2006) |
Abstract
We show that the convex set of separable mixed states of the 2 x 2 system is a body of constant height. This fact is used to prove that the probability to find a random state to be separable equals 2 times the probability to find a random boundary state to be separable, provided the random states are generated uniformly with respect to the Hilbert-Schmidt (Euclidean) distance. An analogous property holds for the set of positive-partial-transpose states for an arbitrary bipartite system.
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"abstract": "We show that the convex set of separable mixed states of the 2 x 2 system is\na body of constant height. This fact is used to prove that the probability to\nfind a random state to be separable equals 2 times the probability to find a\nrandom boundary state to be separable, provided the random states are generated\nuniformly with respect to the Hilbert-Schmidt (Euclidean) distance. An\nanalogous property holds for the set of positive-partial-transpose states for\nan arbitrary bipartite system.",
"arxiv_id": "quant-ph/0509008",
"authors": [
"Stanislaw Szarek",
"Ingemar Bengtsson",
"Karol Zyczkowski"
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"doi": "10.1088/0305-4470/39/5/L02",
"journal_ref": "J. Phys. A 39 L119-L126 (2006)",
"title": "On the structure of the body of states with positive partial transpose",
"url": "https://arxiv.org/abs/quant-ph/0509008"
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