dorsal/arxiv
View SchemaTowards efficient algorithm deciding separability of distributed quantum states
| Authors | Piotr Badziag, Pawel Horodecki, Ryszard Horodecki |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0504041 |
| URL | https://arxiv.org/abs/quant-ph/0504041 |
Abstract
It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly exponentially with the state's rank. Nevertheless, we argue that for generic states, analysis of concurrence matrices essentially reduces the task of solving separability problem in $m \times n$ dimensions to solving a set of linear equations in about $\binom{mn+D-1}{D}$ variables, where $D$ decreases with $mn$ and for large $mn$ it should not exceed 4. Moreover, the same method is also applicable to multipartite states where it is at least equally efficient.
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"abstract": "It is pointed out that separability problem for arbitrary multi-partite\nstates can be fully solved by a finite size, elementary recursive algorithm. In\nthe worse case scenario, the underlying numerical procedure, may grow doubly\nexponentially with the state\u0027s rank. Nevertheless, we argue that for generic\nstates, analysis of concurrence matrices essentially reduces the task of\nsolving separability problem in $m \\times n$ dimensions to solving a set of\nlinear equations in about $\\binom{mn+D-1}{D}$ variables, where $D$ decreases\nwith $mn$ and for large $mn$ it should not exceed 4. Moreover, the same method\nis also applicable to multipartite states where it is at least equally\nefficient.",
"arxiv_id": "quant-ph/0504041",
"authors": [
"Piotr Badziag",
"Pawel Horodecki",
"Ryszard Horodecki"
],
"categories": [
"quant-ph"
],
"title": "Towards efficient algorithm deciding separability of distributed quantum states",
"url": "https://arxiv.org/abs/quant-ph/0504041"
},
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