dorsal/arxiv
View SchemaSeparable approximations of density matrices of composite quantum systems
| Authors | S. Karnas, M. Lewenstein |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0011066 |
| URL | https://arxiv.org/abs/quant-ph/0011066 |
| DOI | 10.1088/0305-4470/34/35/318 |
Abstract
We investigate optimal separable approximations (decompositions) of states rho of bipartite quantum systems A and B of arbitrary dimensions MxN following the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261 (1998)]. Such approximations allow to represent in an optimal way any density operator as a sum of a separable state and an entangled state of a certain form. For two qubit systems (M=N=2) the best separable approximation has a form of a mixture of a separable state and a projector onto a pure entangled state. We formulate a necessary condition that the pure state in the best separable approximation is not maximally entangled. We demonstrate that the weight of the entangled state in the best separable approximation in arbitrary dimensions provides a good entanglement measure. We prove in general for arbitrary M and N that the best separable approximation corresponds to a mixture of a separable and an entangled state which are both unique. We develop also a theory of optimal separable approximations for states with positive partial transpose (PPT states). Such approximations allow to decompose any density operator with positive partial transpose as a sum of a separable state and an entangled PPT state. We discuss procedures of constructing such decompositions.
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"abstract": "We investigate optimal separable approximations (decompositions) of states\nrho of bipartite quantum systems A and B of arbitrary dimensions MxN following\nthe lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261\n(1998)]. Such approximations allow to represent in an optimal way any density\noperator as a sum of a separable state and an entangled state of a certain\nform. For two qubit systems (M=N=2) the best separable approximation has a form\nof a mixture of a separable state and a projector onto a pure entangled state.\nWe formulate a necessary condition that the pure state in the best separable\napproximation is not maximally entangled. We demonstrate that the weight of the\nentangled state in the best separable approximation in arbitrary dimensions\nprovides a good entanglement measure. We prove in general for arbitrary M and N\nthat the best separable approximation corresponds to a mixture of a separable\nand an entangled state which are both unique. We develop also a theory of\noptimal separable approximations for states with positive partial transpose\n(PPT states). Such approximations allow to decompose any density operator with\npositive partial transpose as a sum of a separable state and an entangled PPT\nstate. We discuss procedures of constructing such decompositions.",
"arxiv_id": "quant-ph/0011066",
"authors": [
"S. Karnas",
"M. Lewenstein"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/34/35/318",
"title": "Separable approximations of density matrices of composite quantum systems",
"url": "https://arxiv.org/abs/quant-ph/0011066"
},
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