dorsal/arxiv
View SchemaCompatibility of subsystem states and convex geometry
| Authors | William Hall |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0610031 |
| URL | https://arxiv.org/abs/quant-ph/0610031 |
| DOI | 10.1103/PhysRevA.75.032102 |
Abstract
The subsystem compatibility problem, which concerns the question of whether a set of subsystem states are compatible with a state of the entire system, has received much study. Here we attack the problem from a new angle, utilising the ideas of convexity that have been successfully employed against the separability problem. Analogously to an entanglement witness, we introduce the idea of a compatibility witness, and prove a number of properties about these objects. We show that the subsystem compatibility problem can be solved numerically and efficiently using semidefinite programming, and that the numerical results from this solution can be used to extract exact analytic results, an idea which we use to disprove a conjecture about the subsystem problem made by Butterley et al. [Found. Phys. 36 83 (2006)]. Finally, we consider how the ideas can be used to tackle some important variants of the compatibility problem; in particular, the case of identical particles (known as N-representability in the case of fermions) is considered.
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"abstract": "The subsystem compatibility problem, which concerns the question of whether a\nset of subsystem states are compatible with a state of the entire system, has\nreceived much study. Here we attack the problem from a new angle, utilising the\nideas of convexity that have been successfully employed against the\nseparability problem. Analogously to an entanglement witness, we introduce the\nidea of a compatibility witness, and prove a number of properties about these\nobjects. We show that the subsystem compatibility problem can be solved\nnumerically and efficiently using semidefinite programming, and that the\nnumerical results from this solution can be used to extract exact analytic\nresults, an idea which we use to disprove a conjecture about the subsystem\nproblem made by Butterley et al. [Found. Phys. 36 83 (2006)]. Finally, we\nconsider how the ideas can be used to tackle some important variants of the\ncompatibility problem; in particular, the case of identical particles (known as\nN-representability in the case of fermions) is considered.",
"arxiv_id": "quant-ph/0610031",
"authors": [
"William Hall"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.75.032102",
"title": "Compatibility of subsystem states and convex geometry",
"url": "https://arxiv.org/abs/quant-ph/0610031"
},
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