dorsal/arxiv
View SchemaEvidence for Bound Entangled States with Negative Partial Transpose
| Authors | David P. DiVincenzo, Peter W. Shor, John A. Smolin, Barbara M. Terhal, Ashish V. Thapliyal |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9910026 |
| URL | https://arxiv.org/abs/quant-ph/9910026 |
| DOI | 10.1103/PhysRevA.61.062312 |
| Journal | Phys. Rev. A 61, 062312 (2000) |
Abstract
We exhibit a two-parameter family of bipartite mixed states $\rho_{bc}$, in a $d\otimes d$ Hilbert space, which are negative under partial transposition (NPT), but for which we conjecture that no maximally entangled pure states in $2\otimes 2$ can be distilled by local quantum operations and classical communication (LQ+CC). Evidence for this undistillability is provided by the result that, for certain states in this family, we cannot extract entanglement from any arbitrarily large number of copies of $\rho_{bc}$ using a projection on $2\otimes 2$. These states are canonical NPT states in the sense that any bipartite mixed state in any dimension with NPT can be reduced by LQ+CC operations to an NPT state of the $\rho_{bc}$ form. We show that the main question about the distillability of mixed states can be formulated as an open mathematical question about the properties of composed positive linear maps.
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"abstract": "We exhibit a two-parameter family of bipartite mixed states $\\rho_{bc}$, in a\n$d\\otimes d$ Hilbert space, which are negative under partial transposition\n(NPT), but for which we conjecture that no maximally entangled pure states in\n$2\\otimes 2$ can be distilled by local quantum operations and classical\ncommunication (LQ+CC). Evidence for this undistillability is provided by the\nresult that, for certain states in this family, we cannot extract entanglement\nfrom any arbitrarily large number of copies of $\\rho_{bc}$ using a projection\non $2\\otimes 2$. These states are canonical NPT states in the sense that any\nbipartite mixed state in any dimension with NPT can be reduced by LQ+CC\noperations to an NPT state of the $\\rho_{bc}$ form. We show that the main\nquestion about the distillability of mixed states can be formulated as an open\nmathematical question about the properties of composed positive linear maps.",
"arxiv_id": "quant-ph/9910026",
"authors": [
"David P. DiVincenzo",
"Peter W. Shor",
"John A. Smolin",
"Barbara M. Terhal",
"Ashish V. Thapliyal"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.61.062312",
"journal_ref": "Phys. Rev. A 61, 062312 (2000)",
"title": "Evidence for Bound Entangled States with Negative Partial Transpose",
"url": "https://arxiv.org/abs/quant-ph/9910026"
},
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