dorsal/arxiv
View SchemaSeparability and correlations in composite states based on entropy methods
| Authors | A. K. Rajagopal, R. W. Rendell |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0203124 |
| URL | https://arxiv.org/abs/quant-ph/0203124 |
| DOI | 10.1103/PhysRevA.66.022104 |
Abstract
This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine the entanglement and correlation properties guided by the corresponding calculations of concurrence. It is shown that the entropy difference between that of the composite and its marginal density matrices may be of arbitrary sign except under special circumstances when conditional probability can be defined appropriately. This ambiguity is a consequence of the fact that the overlap matrix elements of the eigenstates of the composite density matrix with those of its marginal density matrices also play important roles in the definitions of probabilities and the associated entropies, along with their respective eigenvalues. The general results are illustrated using pure and mixed state density matrices of two-qubit systems. Two classes of density matrices are found for which the conditional probability can defined: (1) density matrices with commuting decompositions and (2) those which are decohered in the representation where the density matrices of the marginals are diagonal. The first class of states encompass those whose separability is currently understood as due to particular symmetries of the states. The second are a new class of states which are expected to be useful for understanding separability. Examples of entropy functionals of these decohered states including the crucial isospectral case are discussed.
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"abstract": "This work is an enquiry into the circumstances under which entropy methods\ncan give an answer to the questions of both quantum separability and classical\ncorrelations of a composite state. Several entropy functionals are employed to\nexamine the entanglement and correlation properties guided by the corresponding\ncalculations of concurrence. It is shown that the entropy difference between\nthat of the composite and its marginal density matrices may be of arbitrary\nsign except under special circumstances when conditional probability can be\ndefined appropriately. This ambiguity is a consequence of the fact that the\noverlap matrix elements of the eigenstates of the composite density matrix with\nthose of its marginal density matrices also play important roles in the\ndefinitions of probabilities and the associated entropies, along with their\nrespective eigenvalues. The general results are illustrated using pure and\nmixed state density matrices of two-qubit systems. Two classes of density\nmatrices are found for which the conditional probability can defined: (1)\ndensity matrices with commuting decompositions and (2) those which are\ndecohered in the representation where the density matrices of the marginals are\ndiagonal. The first class of states encompass those whose separability is\ncurrently understood as due to particular symmetries of the states. The second\nare a new class of states which are expected to be useful for understanding\nseparability. Examples of entropy functionals of these decohered states\nincluding the crucial isospectral case are discussed.",
"arxiv_id": "quant-ph/0203124",
"authors": [
"A. K. Rajagopal",
"R. W. Rendell"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.022104",
"title": "Separability and correlations in composite states based on entropy methods",
"url": "https://arxiv.org/abs/quant-ph/0203124"
},
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