preprint · arXiv (Cornell University) · 2008

Probability sum rules and consistent quantum histories

Jordan, Thomas F., Chisolm, Eric D.

Cited by 0Open access

Abstract

An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal decoherence are all calculated by using a projection operator to describe each possibility for the state at each time. Weak decoherence requires more sum rules. They bring in additional variables, that require different measurements and a different way to calculate probabilities, and raise questions of operational meaning. The example shows that extending the linearly positive probability formula from weak to minimal decoherence gives probabilities that are different from those calculated in the usual way using the Born and von Neumann rules and a projection operator at each time.

Cite this paper

APA 7

Jordan, T. F., & Chisolm, E. D. (2008). Probability sum rules and consistent quantum histories. arXiv (Cornell University). https://doi.org/10.48550/arxiv.0801.2725

MLA 9

Jordan, Thomas F., and Eric D. Chisolm. “Probability sum rules and consistent quantum histories.” arXiv (Cornell University), 2008, https://doi.org/10.48550/arxiv.0801.2725.

Chicago

Jordan, Thomas F., and Eric D. Chisolm. 2008. “Probability sum rules and consistent quantum histories.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.0801.2725.

Harvard

Jordan, T.F. and Chisolm, E.D. (2008) ‘Probability sum rules and consistent quantum histories’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.0801.2725.

BibTeX

@misc{jordan2008probability,
  title = {{Probability sum rules and consistent quantum histories}},
  author = {Jordan, Thomas F. and Chisolm, Eric D.},
  journal = {arXiv (Cornell University)},
  year = {2008},
  doi = {10.48550/arxiv.0801.2725}
}

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