Incompatible multiple consistent sets of histories and measures of quantumness

Incompatible multiple consistent sets of histories and measures of quantumness In the consistent histories approach to quantum theory probabilities are assigned to histories subject to a consistency condition of negligible interference. The approach has the feature that a given physical situation admits multiple sets of consistent histories that cannot in general be united into a single consistent set, leading to a number of counterintuitive or contrary properties if propositions from different consistent sets are combined indiscriminately. An alternative viewpoint is proposed in which multiple consistent sets are classified according to whether or not there exists any unifying probability for combinations of incompatible sets which replicates the consistent histories result when restricted to a single consistent set. A number of examples are exhibited in which this classification can be made, in some cases with the assistance of the Bell, Clauser-Horne-Shimony-Holt, or Leggett-Garg inequalities together with Fine's theorem. When a unifying probability exists logical deductions in different consistent sets can in fact be combined, an extension of the “single framework rule.” It is argued that this classification coincides with intuitive notions of the boundary between classical and quantum regimes and in particular, the absence of a unifying probability for certain combinations of consistent sets is regarded as a measure of the “quantumness” of the system. The proposed approach and results are closely related to recent work on the classification of quasiprobabilities and this connection is discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Incompatible multiple consistent sets of histories and measures of quantumness

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Incompatible multiple consistent sets of histories and measures of quantumness

Abstract

In the consistent histories approach to quantum theory probabilities are assigned to histories subject to a consistency condition of negligible interference. The approach has the feature that a given physical situation admits multiple sets of consistent histories that cannot in general be united into a single consistent set, leading to a number of counterintuitive or contrary properties if propositions from different consistent sets are combined indiscriminately. An alternative viewpoint is proposed in which multiple consistent sets are classified according to whether or not there exists any unifying probability for combinations of incompatible sets which replicates the consistent histories result when restricted to a single consistent set. A number of examples are exhibited in which this classification can be made, in some cases with the assistance of the Bell, Clauser-Horne-Shimony-Holt, or Leggett-Garg inequalities together with Fine's theorem. When a unifying probability exists logical deductions in different consistent sets can in fact be combined, an extension of the “single framework rule.” It is argued that this classification coincides with intuitive notions of the boundary between classical and quantum regimes and in particular, the absence of a unifying probability for certain combinations of consistent sets is regarded as a measure of the “quantumness” of the system. The proposed approach and results are closely related to recent work on the classification of quasiprobabilities and this connection is discussed.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1050-2947
eISSN
1094-1622
D.O.I.
10.1103/PhysRevA.96.012123
Publisher site
See Article on Publisher Site

Abstract

In the consistent histories approach to quantum theory probabilities are assigned to histories subject to a consistency condition of negligible interference. The approach has the feature that a given physical situation admits multiple sets of consistent histories that cannot in general be united into a single consistent set, leading to a number of counterintuitive or contrary properties if propositions from different consistent sets are combined indiscriminately. An alternative viewpoint is proposed in which multiple consistent sets are classified according to whether or not there exists any unifying probability for combinations of incompatible sets which replicates the consistent histories result when restricted to a single consistent set. A number of examples are exhibited in which this classification can be made, in some cases with the assistance of the Bell, Clauser-Horne-Shimony-Holt, or Leggett-Garg inequalities together with Fine's theorem. When a unifying probability exists logical deductions in different consistent sets can in fact be combined, an extension of the “single framework rule.” It is argued that this classification coincides with intuitive notions of the boundary between classical and quantum regimes and in particular, the absence of a unifying probability for certain combinations of consistent sets is regarded as a measure of the “quantumness” of the system. The proposed approach and results are closely related to recent work on the classification of quasiprobabilities and this connection is discussed.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Jul 25, 2017

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