dorsal/arxiv
View SchemaRelativity of pure states entanglement
| Authors | Karol Zyczkowski, Ingemar Bengtsson |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0103027 |
| URL | https://arxiv.org/abs/quant-ph/0103027 |
| DOI | 10.1006/aphy.2001.6201 |
| Journal | Ann. Phys. 295, 115 (2002) |
Abstract
Entanglement of any pure state of an N times N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of entanglement derived from the generalized entropies of the vector of Schmidt coefficients. For N >= 3 they generate different ordering in the set of pure states and for some states their ordering depends on the measure of entanglement used. This odd-looking property is acceptable, since these incomparable states cannot be transformed to each other with unit efficiency by any local operation. In analogy to special relativity the set of pure states equivalent under local unitaries has a causal structure so that at each point the set splits into three parts: the 'Future', the 'Past' and the set of noncomparable states.
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"abstract": "Entanglement of any pure state of an N times N bi-partite quantum system may\nbe characterized by the vector of coefficients arising by its Schmidt\ndecomposition. We analyze various measures of entanglement derived from the\ngeneralized entropies of the vector of Schmidt coefficients. For N \u003e= 3 they\ngenerate different ordering in the set of pure states and for some states their\nordering depends on the measure of entanglement used. This odd-looking property\nis acceptable, since these incomparable states cannot be transformed to each\nother with unit efficiency by any local operation. In analogy to special\nrelativity the set of pure states equivalent under local unitaries has a causal\nstructure so that at each point the set splits into three parts: the \u0027Future\u0027,\nthe \u0027Past\u0027 and the set of noncomparable states.",
"arxiv_id": "quant-ph/0103027",
"authors": [
"Karol Zyczkowski",
"Ingemar Bengtsson"
],
"categories": [
"quant-ph"
],
"doi": "10.1006/aphy.2001.6201",
"journal_ref": "Ann. Phys. 295, 115 (2002)",
"title": "Relativity of pure states entanglement",
"url": "https://arxiv.org/abs/quant-ph/0103027"
},
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