The Choi–Jamiołkowski isomorphism and covariant quantum channels
Copyright policy )The Choi–Jamiołkowski isomorphism and covariant quantum channels
A generalization of the Choi-Jamiolkowski isomorphism for completely positive maps between operator algebras is introduced. Particular emphasis is placed on the case of normal unital completely positive maps defined between von Neumann algebras. This generalization is applied especially to the study of maps which are covariant under actions of a symmetry group. We highlight with the example of, e.g., phase-shift-covariant quantum channels the ease of this method in particular in the case of a compact symmetry group. We also discuss the case of channels which are covariant under actions of the Euclidean group of rigid motions in 3 dimensions.
24 pages; an error in an earlier version has been corrected
- National University of Singapore Singapore
- Centre for Quantum Technologies Singapore
Operator algebra methods applied to problems in quantum theory, Quantum Physics, \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, operator algebras in quantum theory, FOS: Physical sciences, Mathematical Physics (math-ph), quantum channels, Applications of group representations to physics and other areas of science, 20C35, 22D25, 46L06, 46L55, 81R15, Quantum theory, covariance, Tensor products of \(C^*\)-algebras, Noncommutative dynamical systems, Quantum Physics (quant-ph), completely positive maps, Mathematical Physics
Operator algebra methods applied to problems in quantum theory, Quantum Physics, \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations, operator algebras in quantum theory, FOS: Physical sciences, Mathematical Physics (math-ph), quantum channels, Applications of group representations to physics and other areas of science, 20C35, 22D25, 46L06, 46L55, 81R15, Quantum theory, covariance, Tensor products of \(C^*\)-algebras, Noncommutative dynamical systems, Quantum Physics (quant-ph), completely positive maps, Mathematical Physics
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