dorsal/arxiv
View SchemaA (5,5) and (6,6) PPT edge state
| Authors | Lieven Clarisse |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603283 |
| URL | https://arxiv.org/abs/quant-ph/0603283 |
| DOI | 10.1016/j.physleta.2006.07.045 |
| Journal | Physics Letters A 359 (2006) 603-607 |
Abstract
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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"abstract": "Entangled states with a positive partial transpose (PPTES) have interest both\nin quantum information and in the theory of positive maps. In $3\\otimes 3$\nthere is a conjecture by Sanpera, Bru{\\ss} and Lewenstein [PRA, 63, 050301]\nthat all PPTES have Schmidt number two (or equivalently that every 2-positive\nmap between $3\\times 3$ matrices is decomposable). In order to prove or\ndisprove the conjecture it is sufficient to look at edge PPTES. Here the rank m\nof the PPTES and the rank n of its partial transpose seem to play an important\nrole. Until recently all known examples of edge PPTES had ranks (4,4) or (6,7).\nIn a recent paper Ha and Kye [quant-ph/0509079] managed to find edge PPTES for\nall ranks except (5,5) and (6,6). Here we complement their work and present\nedge PPTES with those ranks.",
"arxiv_id": "quant-ph/0603283",
"authors": [
"Lieven Clarisse"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.physleta.2006.07.045",
"journal_ref": "Physics Letters A 359 (2006) 603-607",
"title": "A (5,5) and (6,6) PPT edge state",
"url": "https://arxiv.org/abs/quant-ph/0603283"
},
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