2006/03/31 by Lieven Clarisse · 42 citations
Computer Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Bound state #Combinatorics #Computer science #Conjecture #Enhanced Data Rates for GSM Evolution #Mathematics #Physics #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Theoretical physics #quant-ph
paper · pdf · doi:10.1016/j.physleta.2006.07.045
published in Physics Letters A 359(6), 603-607 (Elsevier BV) · 5 pages, comments welcome
arxiv created 2006/03/31 · openalex publication_date 2006/08/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Entangled states with a positive partial transpose (PPTES) have interest both in quantum information and in the theory of positive maps. In 3⊗ 3 there is a conjecture by Sanpera, Bruß and Lewenstein [PRA, 63, 050301] that all PPTES have Schmidt number two (or equivalently that every 2-positive map between 3× 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.