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Beyond the standard entropic inequalities : stronger scalar separability criteria and their applications
Augusiak, Remigiusz (Gdańsk University of Technology. Faculty of Applied Physics and Mathematics)
Stasinska, Julia (Gdańsk University of Technology. Faculty of Applied Physics and Mathematics)
Horodecki, Pawel (Gdańsk University of Technology. Faculty of Applied Physics and Mathematics)
American Physical Society

Data: 2008
Resum: Recently it was shown that if a given state fulfils the reduction criterion, it must also satisfy the known entropic inequalities. The natural question arises as to whether it is possible to derive some scalar inequalities stronger than the entropic ones, assuming that stronger criteria based on positive but not completely positive maps are satisfied. In the present paper we show that if certain conditions hold, the extended reduction criterion [H. -P. Breuer, Phys. Rev. Lett 97, 080501 (2006); W. Hall, J. Phys. A 40, 6183 (2007)] leads to some entropiclike inequalities, much stronger than their entropic counterparts. The comparison of the derived inequalities with other separability criteria shows that such an approach might lead to strong scalar criteria detecting both distillable and bound entanglement. In particular, in the case of SO(3)-invariant states it is shown that the present inequalities detect entanglement in regions, in which linear entanglement witnesses based on the extended reduction map fail. It should also be emphasized that in the case of 2⊗d states the derived inequalities detect entanglement efficiently, while the extended reduction maps are useless, when acting on the qubit subsystem. Moreover, there is a natural way to construct a many-copy entanglement witnesses based on the derived inequalities so, in principle, there is a possibility of experimental realization. Some open problems and possibilities for further research are outlined.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: Article ; recerca ; Versió publicada
Publicat a: Physical review. A, Vol. 77, Issue 1 (January 2008) , p. 012333-1-012333-14, ISSN 1050-2947

DOI: 10.1103/PhysRevA.77.012333

14 p, 754.5 KB

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