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| related topics |
| {entanglement, phys, rev} |
| {let, theorem, proof} |
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Separability analyses of two-qubit density matrices
Paul B. Slater
abstract: We pursue a number of analytical directions, motivated to some extent
initially by the possibility of developing a methodology for formally proving
or disproving a certain conjecture of quantum-theoretical relevance
(quant-ph/0308037). It asserts that the 15-dimensional volume occupied by the
separable two-qubit density matrices is (\sqrt{2}-1)/3, as measured in terms of
the statistical distinguishability metric (four times the Bures or minimal
monotone metric). Somewhat disappointingly, however, the several various
analyses that we report, though we hope of independent/autonomous interest,
appear to provide small indication of how to definitively resolve the
conjecture. Among our studies here are ones of: (1) the Bures volumes of the
two-dimensional sections of Bloch vectors for a number of the
Jakobczyk-Siennicki two-qubit scenarios; (2) the structure of certain convex
polytopes of separable density matrices; and (3) the diagonalization of 15 x 15
Bures metric tensors.
- oai_identifier:
- oai:arXiv.org:quant-ph/0408157
- categories:
- quant-ph
- comments:
- 19 pages, 9 figures
- arxiv_id:
- quant-ph/0408157
- created:
- 2004-08-25
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