dorsal/arxiv
View SchemaOn independent permutation separability criteria
| Authors | Lieven Clarisse, Pawel Wocjan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0504160 |
| URL | https://arxiv.org/abs/quant-ph/0504160 |
| Journal | Quantum Information and Computation, Vol. 6, No. 3 (2006) 277-288 |
Abstract
Recently P. Wocjan and M. Horodecki [quant-ph/0503129] gave a characterization of combinatorially independent permutation separability criteria. Combinatorial independence is a necessary condition for permutations to yield truly independent criteria meaning that that no criterion is strictly stronger that any other. In this paper we observe that some of these criteria are still dependent and analyze why these dependencies occur. To remove them we introduce an improved necessary condition and give a complete classification of the remaining permutations. We conjecture that the remaining class of criteria only contains truly independent permutation separability criteria. Our conjecture is based on the proof that for two, three and four parties all these criteria are truly independent and on numerical verification of their independence for up to 8 parties. It was commonly believed that for three parties there were 9 independent criteria, here we prove that there are exactly 6 independent criteria for three parties and 22 for four parties.
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"abstract": "Recently P. Wocjan and M. Horodecki [quant-ph/0503129] gave a\ncharacterization of combinatorially independent permutation separability\ncriteria. Combinatorial independence is a necessary condition for permutations\nto yield truly independent criteria meaning that that no criterion is strictly\nstronger that any other. In this paper we observe that some of these criteria\nare still dependent and analyze why these dependencies occur. To remove them we\nintroduce an improved necessary condition and give a complete classification of\nthe remaining permutations. We conjecture that the remaining class of criteria\nonly contains truly independent permutation separability criteria. Our\nconjecture is based on the proof that for two, three and four parties all these\ncriteria are truly independent and on numerical verification of their\nindependence for up to 8 parties. It was commonly believed that for three\nparties there were 9 independent criteria, here we prove that there are exactly\n6 independent criteria for three parties and 22 for four parties.",
"arxiv_id": "quant-ph/0504160",
"authors": [
"Lieven Clarisse",
"Pawel Wocjan"
],
"categories": [
"quant-ph"
],
"journal_ref": "Quantum Information and Computation, Vol. 6, No. 3 (2006) 277-288",
"title": "On independent permutation separability criteria",
"url": "https://arxiv.org/abs/quant-ph/0504160"
},
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