dorsal/arxiv
View SchemaSimplifying monotonicity conditions for entanglement measures
| Authors | Michal Horodecki |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412210 |
| URL | https://arxiv.org/abs/quant-ph/0412210 |
| Journal | Open Syst. Inf. Dyn. 12, 231 (2005) |
Abstract
We show that for a convex function the following, rather modest conditions, are equivalent to monotonicity under local operations and classical communication. The conditions are: 1)invariance under local unitaries, 2) invariance under adding local ancilla in arbitrary state 3) on mixtures of states possessing local orthogonal flags the function is equal to its average. The result holds for multipartite systems. It is intriguing that the obtained conditions are equalities. The only inequality is hidden in the condition of convexity.
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"abstract": "We show that for a convex function the following, rather modest conditions,\nare equivalent to monotonicity under local operations and classical\ncommunication. The conditions are: 1)invariance under local unitaries, 2)\ninvariance under adding local ancilla in arbitrary state 3) on mixtures of\nstates possessing local orthogonal flags the function is equal to its average.\nThe result holds for multipartite systems. It is intriguing that the obtained\nconditions are equalities. The only inequality is hidden in the condition of\nconvexity.",
"arxiv_id": "quant-ph/0412210",
"authors": [
"Michal Horodecki"
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"journal_ref": "Open Syst. Inf. Dyn. 12, 231 (2005)",
"title": "Simplifying monotonicity conditions for entanglement measures",
"url": "https://arxiv.org/abs/quant-ph/0412210"
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