dorsal/arxiv
View SchemaChecking $2 \times M$ separability via semidefinite programming
| Authors | Hugo J. Woerdeman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0301058 |
| URL | https://arxiv.org/abs/quant-ph/0301058 |
| DOI | 10.1103/PhysRevA.67.010303 |
Abstract
In this paper we propose a sequence of tests which gives a definitive test for checking $2\times M$ separability. The test is definitive in the sense that each test corresponds to checking membership in a cone, and that the closure of the union of all these cones consists exactly of {\it all} $2 \times M$ separable states. Membership in each single cone may be checked via semidefinite programming, and is thus a tractable problem. This sequential test comes about by considering the dual problem, the characterization of all positive maps acting ${\mathbb C}^{2 \times 2} \to {\mathbb C}^{M\times M}$. The latter in turn is solved by characterizing all positive quadratic matrix polynomials in a complex variable.
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"abstract": "In this paper we propose a sequence of tests which gives a definitive test\nfor checking $2\\times M$ separability. The test is definitive in the sense that\neach test corresponds to checking membership in a cone, and that the closure of\nthe union of all these cones consists exactly of {\\it all} $2 \\times M$\nseparable states. Membership in each single cone may be checked via\nsemidefinite programming, and is thus a tractable problem. This sequential test\ncomes about by considering the dual problem, the characterization of all\npositive maps acting ${\\mathbb C}^{2 \\times 2} \\to {\\mathbb C}^{M\\times M}$.\nThe latter in turn is solved by characterizing all positive quadratic matrix\npolynomials in a complex variable.",
"arxiv_id": "quant-ph/0301058",
"authors": [
"Hugo J. Woerdeman"
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],
"doi": "10.1103/PhysRevA.67.010303",
"title": "Checking $2 \\times M$ separability via semidefinite programming",
"url": "https://arxiv.org/abs/quant-ph/0301058"
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