Partial decoherence of histories and the Diósi test

Partial decoherence of histories and the Diósi test In the decoherent histories approach to quantum theory, attention focuses on the conditions under which probabilities may be assigned to sets of quantum histories. A variety of conditions have been proposed, but the most important one is decoherence, which means that the interference between every pair of histories in the set is zero. Weaker conditions have been considered, such as consistency, or linear positivity, but these are ruled out by the requirement of consistent composition of subsystems, proposed by Diósi. Here we propose a new condition which we call partial decoherence, and is the requirement that every history has zero interference with its negation. This is weaker than decoherence and stronger than linear positivity (but its relation to consistency is less simply defined—it is neither stronger nor weaker). Most importantly, it satisfies the Diósi condition. A strengthened Diósi condition is proposed, which partial decoherence narrowly fails, due to an unusual property of inhomogeneous histories. In an appendix an example is given of a set of histories which are consistent but not decoherent. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Partial decoherence of histories and the Diósi test

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Publisher
Springer Journals
Copyright
Copyright © 2009 by Springer Science+Business Media, LLC
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/s11128-009-0134-9
Publisher site
See Article on Publisher Site

Abstract

In the decoherent histories approach to quantum theory, attention focuses on the conditions under which probabilities may be assigned to sets of quantum histories. A variety of conditions have been proposed, but the most important one is decoherence, which means that the interference between every pair of histories in the set is zero. Weaker conditions have been considered, such as consistency, or linear positivity, but these are ruled out by the requirement of consistent composition of subsystems, proposed by Diósi. Here we propose a new condition which we call partial decoherence, and is the requirement that every history has zero interference with its negation. This is weaker than decoherence and stronger than linear positivity (but its relation to consistency is less simply defined—it is neither stronger nor weaker). Most importantly, it satisfies the Diósi condition. A strengthened Diósi condition is proposed, which partial decoherence narrowly fails, due to an unusual property of inhomogeneous histories. In an appendix an example is given of a set of histories which are consistent but not decoherent.

Journal

Quantum Information ProcessingSpringer Journals

Published: Sep 25, 2009

References

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