A comparative study of relative entropy of entanglement, concurrence and negativity

The problem of ordering of two-qubit states imposed by the relative entropy of entanglement (E) in comparison with the concurrence (C) and negativity (N) is studied. Analytical examples of states consistently and inconsistently ordered by the entanglement measures are given. In particular, the state...

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Bibliographic Details
Published inJournal of optics. B, Quantum and semiclassical optics Vol. 6; no. 12; pp. 542 - 548
Main Authors Miranowicz, Adam, Grudka, Andrzej
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 01.12.2004
Institute of Physics
Subjects
Classical and quantum physics: mechanics and fields
Exact sciences and technology
Foundations, theory of measurement, miscellaneous theories (including aharonov-bohm effect, bell inequalities, berry's phase)
Physics
Quantum mechanics
Theoretical study
Ordering
Quantum entanglement
Bell inequality
Relative entropy
Analytical method
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ISSN1464-4266
1741-3575
DOI10.1088/1464-4266/6/12/009

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Summary:The problem of ordering of two-qubit states imposed by the relative entropy of entanglement (E) in comparison with the concurrence (C) and negativity (N) is studied. Analytical examples of states consistently and inconsistently ordered by the entanglement measures are given. In particular, the states for which any of the three measures imposes order opposite to that given by the other two measures are described. Moreover, examples are given of pairs of the states for which (i) and but is different from , (ii) and but differs from , (iii) , and ; and (iv) states having the same E, C and N but still violating the Bell-Clauser-Horne-Shimony-Holt inequality to different degrees.
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ISSN:1464-4266
1741-3575
DOI:10.1088/1464-4266/6/12/009