A (5,5) and (6,6) PPT edge state

Details A (5,5) and (6,6) PPT edge state A (5,5) and (6,6) PPT edge state

2006-03-31

arxiv.org/abs/quant-ph/0603283v1

Physics Letters A 359 (2006) 603-607

Physics

Quantum Physics

5 pages, comments welcome

Scientific paper

10.1016/j.physleta.2006.07.045

Entangled states with a positive partial transpose (PPTES) have interest both in quantum information and in the theory of positive maps. In $3\otimes 3$ there is a conjecture by Sanpera, Bru{\ss} and Lewenstein [PRA, 63, 050301] that all PPTES have Schmidt number two (or equivalently that every 2-positive map between $3\times 3$ matrices is decomposable). In order to prove or disprove the conjecture it is sufficient to look at edge PPTES. Here the rank m of the PPTES and the rank n of its partial transpose seem to play an important role. Until recently all known examples of edge PPTES had ranks (4,4) or (6,7). In a recent paper Ha and Kye [quant-ph/0509079] managed to find edge PPTES for all ranks except (5,5) and (6,6). Here we complement their work and present edge PPTES with those ranks.

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