dorsal/arxiv
View SchemaStructure and Parametrization of Stochastic Maps of Density Matrices
| Authors | E. C. G. Sudarshan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0109158 |
| URL | https://arxiv.org/abs/quant-ph/0109158 |
Abstract
The generic linear evolution of the density matrix of a system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear convex set that may be viewed as supermatrices. The property of hermiticity of density matrices renders an associated supermatrix hermitian and hence diagonalizable; but the positivity of the density matrix does not make this associated supermatrix positive. If it is positive, the map is called completely positive and they have a simple parametrization. This is extended to all positive (not completely positive) maps. A contraction of a norm-preserving map of the combined system can be contracted to obtain all dynamical maps. The reconstruction of the extended dynamics is given.
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"abstract": "The generic linear evolution of the density matrix of a system with a\nfinite-dimensional state space is by stochastic maps which take a density\nmatrix linearly into the set of density matrices. These dynamical stochastic\nmaps form a linear convex set that may be viewed as supermatrices. The property\nof hermiticity of density matrices renders an associated supermatrix hermitian\nand hence diagonalizable; but the positivity of the density matrix does not\nmake this associated supermatrix positive. If it is positive, the map is called\ncompletely positive and they have a simple parametrization. This is extended to\nall positive (not completely positive) maps. A contraction of a norm-preserving\nmap of the combined system can be contracted to obtain all dynamical maps. The\nreconstruction of the extended dynamics is given.",
"arxiv_id": "quant-ph/0109158",
"authors": [
"E. C. G. Sudarshan"
],
"categories": [
"quant-ph"
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"title": "Structure and Parametrization of Stochastic Maps of Density Matrices",
"url": "https://arxiv.org/abs/quant-ph/0109158"
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