Nuclear numerical range and quantum error correction codes for non-unitary noise models

Nuclear numerical range and quantum error correction codes for non-unitary noise models We introduce a notion of nuclear numerical range defined as the set of expectation values of a given operator A among normalized pure states, which belong to the nucleus of an auxiliary operator Z. This notion proves to be applicable to investigate models of quantum noise with block-diagonal structure of the corresponding Kraus operators. The problem of constructing a suitable quantum error correction code for this model can be restated as a geometric problem of finding intersection points of certain sets in the complex plane. This technique, worked out in the case of two-qubit systems, can be generalized for larger dimensions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Nuclear numerical range and quantum error correction codes for non-unitary noise models

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Publisher
Springer US
Copyright
Copyright © 2016 by The Author(s)
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/s11128-016-1484-8
Publisher site
See Article on Publisher Site

Abstract

We introduce a notion of nuclear numerical range defined as the set of expectation values of a given operator A among normalized pure states, which belong to the nucleus of an auxiliary operator Z. This notion proves to be applicable to investigate models of quantum noise with block-diagonal structure of the corresponding Kraus operators. The problem of constructing a suitable quantum error correction code for this model can be restated as a geometric problem of finding intersection points of certain sets in the complex plane. This technique, worked out in the case of two-qubit systems, can be generalized for larger dimensions.

Journal

Quantum Information ProcessingSpringer Journals

Published: Dec 10, 2016

References

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