Testing the monogamy relations via rank2 mixtures
Abstract
We introduce two tanglebased fourparty entanglement measures t_{1} and t_{2}, and two negativitybased measures n_{1} and n_{2}, which are derived from the monogamy relations. These measures are computed for three fourqubit maximally entangled and W states explicitly. We also compute these measures for the rank2 mixture ρ_{4}=p  GHZ_{4}>< GHZ_{4}+(1 p )  W_{4}>< W_{4} by finding the corresponding optimal decompositions. It turns out that t_{1}(ρ_{4}) is trivial and the corresponding optimal decomposition is equal to the spectral decomposition. Probably, this triviality is a sign of the fact that the corresponding monogamy inequality is not sufficiently tight. We fail to compute t_{2}(ρ_{4}) due to the difficulty in the calculation of the residual entanglement. The negativitybased measures n_{1}(ρ_{4}) and n_{2}(ρ_{4}) are explicitly computed and the corresponding optimal decompositions are also derived explicitly.
 Publication:

Physical Review A
 Pub Date:
 October 2016
 DOI:
 10.1103/PhysRevA.94.042330
 arXiv:
 arXiv:1607.00135
 Bibcode:
 2016PhRvA..94d2330J
 Keywords:

 Quantum Physics
 EPrint:
 24 pages, 9 figures. arXiv admin note: text overlap with arXiv:1505.06261 V2: version to appear in PRA