dorsal/arxiv
View SchemaSeparable-entangled frontier in a bipartite harmonic system
| Authors | Constantino Tsallis, Domingo Prato, Celia Anteneodo |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0202077 |
| URL | https://arxiv.org/abs/quant-ph/0202077 |
| DOI | 10.1140/epjb/e2002-00343-2 |
Abstract
We consider a statistical mixture of two identical harmonic oscillators which is characterized by four parameters, namely, the concentrations (x and y) of diagonal and nondiagonal bipartite states, and their associated thermal-like noises (T/a and T, respectively). The fully random mixture of two spins 1/2 as well as the Einstein-Podolsky-Rosen (EPR) state are recovered as particular instances. By using the conditional nonextensive entropy as introduced by Abe and Rajagopal, we calculate the separable-entangled frontier. Although this procedure is known to provide a necessary but in general not sufficient condition for separability, it does recover, in the particular case x=T=0 (for all a), the 1/3 exact result known as Peres' criterion. This is an indication of reliability of the calculation of the frontier in the entire parameter space. The x=0 frontier remarkably resembles to the critical line associated with standard diluted ferromagnetism where the entangled region corresponds to the ordered one and the separable region to the paramagnetic one. The entangled region generically shrinks for increasing T or increasing a.
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"abstract": "We consider a statistical mixture of two identical harmonic oscillators which\nis characterized by four parameters, namely, the concentrations (x and y) of\ndiagonal and nondiagonal bipartite states, and their associated thermal-like\nnoises (T/a and T, respectively). The fully random mixture of two spins 1/2 as\nwell as the Einstein-Podolsky-Rosen (EPR) state are recovered as particular\ninstances. By using the conditional nonextensive entropy as introduced by Abe\nand Rajagopal, we calculate the separable-entangled frontier. Although this\nprocedure is known to provide a necessary but in general not sufficient\ncondition for separability, it does recover, in the particular case x=T=0 (for\nall a), the 1/3 exact result known as Peres\u0027 criterion. This is an indication\nof reliability of the calculation of the frontier in the entire parameter\nspace. The x=0 frontier remarkably resembles to the critical line associated\nwith standard diluted ferromagnetism where the entangled region corresponds to\nthe ordered one and the separable region to the paramagnetic one. The entangled\nregion generically shrinks for increasing T or increasing a.",
"arxiv_id": "quant-ph/0202077",
"authors": [
"Constantino Tsallis",
"Domingo Prato",
"Celia Anteneodo"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech"
],
"doi": "10.1140/epjb/e2002-00343-2",
"title": "Separable-entangled frontier in a bipartite harmonic system",
"url": "https://arxiv.org/abs/quant-ph/0202077"
},
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