dorsal/arxiv
View SchemaConstrained bounds on measures of entanglement
| Authors | Animesh Datta, Steven T. Flammia, Anil Shaji, Carlton M. Caves |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612049 |
| URL | https://arxiv.org/abs/quant-ph/0612049 |
| DOI | 10.1103/PhysRevA.75.062117 |
| Journal | Phys. Rev. A 75, 062117 (2007) |
Abstract
Entanglement measures constructed from two positive, but not completely positive maps on density operators are used as constraints in placing bounds on the entanglement of formation, the tangle, and the concurrence of 4 x N mixed states. The maps are the partial transpose map and the $\Phi$-map introduced by Breuer [H.-P. Breuer, Phys. Rev. Lett. 97, 080501 (2006)]. The norm-based entanglement measures constructed from these two maps, called negativity and $\Phi$-negativity, respectively, lead to two sets of bounds on the entanglement of formation, the tangle, and the concurrence. We compare these bounds and identify the sets of 4 x N density operators for which the bounds from one constraint are better than the bounds from the other. In the process, we present a new derivation of the already known bound on the concurrence based on the negativity. We compute new bounds on the three measures of entanglement using both the constraints simultaneously. We demonstrate how such doubly constrained bounds can be constructed. We discuss extensions of our results to bipartite states of higher dimensions and with more than two constraints.
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"abstract": "Entanglement measures constructed from two positive, but not completely\npositive maps on density operators are used as constraints in placing bounds on\nthe entanglement of formation, the tangle, and the concurrence of 4 x N mixed\nstates. The maps are the partial transpose map and the $\\Phi$-map introduced by\nBreuer [H.-P. Breuer, Phys. Rev. Lett. 97, 080501 (2006)]. The norm-based\nentanglement measures constructed from these two maps, called negativity and\n$\\Phi$-negativity, respectively, lead to two sets of bounds on the entanglement\nof formation, the tangle, and the concurrence. We compare these bounds and\nidentify the sets of 4 x N density operators for which the bounds from one\nconstraint are better than the bounds from the other. In the process, we\npresent a new derivation of the already known bound on the concurrence based on\nthe negativity. We compute new bounds on the three measures of entanglement\nusing both the constraints simultaneously. We demonstrate how such doubly\nconstrained bounds can be constructed. We discuss extensions of our results to\nbipartite states of higher dimensions and with more than two constraints.",
"arxiv_id": "quant-ph/0612049",
"authors": [
"Animesh Datta",
"Steven T. Flammia",
"Anil Shaji",
"Carlton M. Caves"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.75.062117",
"journal_ref": "Phys. Rev. A 75, 062117 (2007)",
"title": "Constrained bounds on measures of entanglement",
"url": "https://arxiv.org/abs/quant-ph/0612049"
},
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