dorsal/arxiv
View SchemaSeparability in 2xN composite quantum systems
| Authors | B. Kraus, J. I. Cirac, S. Karnas, M. Lewenstein |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9912010 |
| URL | https://arxiv.org/abs/quant-ph/9912010 |
| DOI | 10.1103/PhysRevA.61.062302 |
| Journal | Phys.Rev.A 61, 062302 (2000) |
Abstract
We analyze the separability properties of density operators supported on $\C^2\otimes \C^N$ whose partial transposes are positive operators. We show that if the rank of $\rho$ equals N then it is separable, and that bound entangled states have rank larger than N. We also give a separability criterion for a generic density operator such that the sum of its rank and the one of its partial transpose does not exceed 3N. If it exceeds this number we show that one can subtract product vectors until decreasing it to 3N, while keeping the positivity of $\rho$ and its partial transpose. This automatically gives us a sufficient criterion for separability for general density operators. We also prove that all density operators that remain invariant after partial transposition with respect to the first system are separable.
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"abstract": "We analyze the separability properties of density operators supported on\n$\\C^2\\otimes \\C^N$ whose partial transposes are positive operators. We show\nthat if the rank of $\\rho$ equals N then it is separable, and that bound\nentangled states have rank larger than N. We also give a separability criterion\nfor a generic density operator such that the sum of its rank and the one of its\npartial transpose does not exceed 3N. If it exceeds this number we show that\none can subtract product vectors until decreasing it to 3N, while keeping the\npositivity of $\\rho$ and its partial transpose. This automatically gives us a\nsufficient criterion for separability for general density operators. We also\nprove that all density operators that remain invariant after partial\ntransposition with respect to the first system are separable.",
"arxiv_id": "quant-ph/9912010",
"authors": [
"B. Kraus",
"J. I. Cirac",
"S. Karnas",
"M. Lewenstein"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.61.062302",
"journal_ref": "Phys.Rev.A 61, 062302 (2000)",
"title": "Separability in 2xN composite quantum systems",
"url": "https://arxiv.org/abs/quant-ph/9912010"
},
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