2007/07/31 by Remigiusz Augusiak, Julia Stasińska, Paweł Horodecki +1
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physreva.77.012333
published as Physical Review A 77, 012333 (2008) · 15 Pages, RevTex, 7 figures, some new results were added, few references changed, typos corrected
openalex publication_date 2008/01/28 · arxiv created 2008/02/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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\ensuremath\bigotimesd 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.