dorsal/arxiv
View SchemaGaussian relative entropy of entanglement
| Authors | Xiao-yu Chen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0402109 |
| URL | https://arxiv.org/abs/quant-ph/0402109 |
| DOI | 10.1103/PhysRevA.71.062320 |
| Journal | Phys. Rev. A, 71, 062320 (2005) |
Abstract
For two gaussian states with given correlation matrices, in order that relative entropy between them is practically calculable, I in this paper describe the ways of transforming the correlation matrix to matrix in the exponential density operator. Gaussian relative entropy of entanglement is proposed as the minimal relative entropy of the gaussian state with respect to separable gaussian state set. I prove that gaussian relative entropy of entanglement achieves when the separable gaussian state is at the border of separable gaussian state set and inseparable gaussian state set. For two mode gaussian states, the calculation of gaussian relative entropy of entanglement is greatly simplified from searching for a matrix with 10 undetermined parameters to 3 variables. The two mode gaussian states are classified as four types, numerical evidence strongly suggests that gaussian relative entropy of entanglement for each type is realized by the separable state within the same type.For symmetric gaussian state it is strictly proved that it is achieved by symmetric gaussian state.
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"abstract": "For two gaussian states with given correlation matrices, in order that\nrelative entropy between them is practically calculable, I in this paper\ndescribe the ways of transforming the correlation matrix to matrix in the\nexponential density operator. Gaussian relative entropy of entanglement is\nproposed as the minimal relative entropy of the gaussian state with respect to\nseparable gaussian state set. I prove that gaussian relative entropy of\nentanglement achieves when the separable gaussian state is at the border of\nseparable gaussian state set and inseparable gaussian state set. For two mode\ngaussian states, the calculation of gaussian relative entropy of entanglement\nis greatly simplified from searching for a matrix with 10 undetermined\nparameters to 3 variables. The two mode gaussian states are classified as four\ntypes, numerical evidence strongly suggests that gaussian relative entropy of\nentanglement for each type is realized by the separable state within the same\ntype.For symmetric gaussian state it is strictly proved that it is achieved by\nsymmetric gaussian state.",
"arxiv_id": "quant-ph/0402109",
"authors": [
"Xiao-yu Chen"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.71.062320",
"journal_ref": "Phys. Rev. A, 71, 062320 (2005)",
"title": "Gaussian relative entropy of entanglement",
"url": "https://arxiv.org/abs/quant-ph/0402109"
},
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