On a Parametrization of Purifications of a Qubit

On a Parametrization of Purifications of a Qubit This work provides, constructively, explicit one–one parametrizations of all purifications of a mixed state in dimension 2 and all joint purifications, if any, of two mixed states in the same dimension. The former is parametrized by SO(3, R), while the latter is parametrized by SO(2, R), except when the state being purified is already pure. These parametrizations are derived without any passage to the spectral decompositions of the state(s) being purified. Using this, we show how to calculate certain measures of quantum information. The appendix considers an alternative one–one parametrization of mixed states in C2 ⊗ C2, which provides a different explicit construction of joint purifications. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

On a Parametrization of Purifications of a Qubit

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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2002 by Plenum Publishing Corporation
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.
10.1023/A:1023473931663
Publisher site
See Article on Publisher Site

Abstract

This work provides, constructively, explicit one–one parametrizations of all purifications of a mixed state in dimension 2 and all joint purifications, if any, of two mixed states in the same dimension. The former is parametrized by SO(3, R), while the latter is parametrized by SO(2, R), except when the state being purified is already pure. These parametrizations are derived without any passage to the spectral decompositions of the state(s) being purified. Using this, we show how to calculate certain measures of quantum information. The appendix considers an alternative one–one parametrization of mixed states in C2 ⊗ C2, which provides a different explicit construction of joint purifications.

Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 13, 2004

References

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