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Relativity of Pure States Entanglement

✍ Scribed by Karol Życzkowski; Ingemar Bengtsson

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
293 KB
Volume
295
Category
Article
ISSN
0003-4916

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✦ Synopsis

Entanglement of any pure state of an N × 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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