The operator-sum-difference representation of a quantum noise channel

The operator-sum-difference representation of a quantum noise channel When a model for quantum noise is exactly solvable, a Kraus (or operator-sum) representation can be derived from the spectral decomposition of the Choi matrix for the channel. More generally, a Kraus representation can be obtained from any positive-sum (or ensemble) decomposition of the matrix. Here we extend this idea to any Hermitian-sum decomposition. This yields what we call the “operator-sum-difference” (OSD) representation, in which the channel can be represented as the sum and difference of “subchannels.” As one application, the subchannels can be chosen to be analytically diagonalizable, even if the parent channel is not (on account of the Abel-Galois irreducibility theorem), though in this case the number of the OSD representation operators may exceed the channel rank. Our procedure is applicable to general Hermitian (completely positive or non-completely positive) maps and can be extended to the more general, linear maps. As an illustration of the application, we derive an OSD representation for a two-qubit amplitude-damping channel. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

The operator-sum-difference representation of a quantum noise channel

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Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-0965-5
Publisher site
See Article on Publisher Site

Abstract

When a model for quantum noise is exactly solvable, a Kraus (or operator-sum) representation can be derived from the spectral decomposition of the Choi matrix for the channel. More generally, a Kraus representation can be obtained from any positive-sum (or ensemble) decomposition of the matrix. Here we extend this idea to any Hermitian-sum decomposition. This yields what we call the “operator-sum-difference” (OSD) representation, in which the channel can be represented as the sum and difference of “subchannels.” As one application, the subchannels can be chosen to be analytically diagonalizable, even if the parent channel is not (on account of the Abel-Galois irreducibility theorem), though in this case the number of the OSD representation operators may exceed the channel rank. Our procedure is applicable to general Hermitian (completely positive or non-completely positive) maps and can be extended to the more general, linear maps. As an illustration of the application, we derive an OSD representation for a two-qubit amplitude-damping channel.

Journal

Quantum Information ProcessingSpringer Journals

Published: Mar 12, 2015

References

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