Quantum conditional probabilities

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Pérez, Ignacio and Luis Aina, Alfredo (2022) Quantum conditional probabilities. Journal of physics A: Mathematical and theoretical, 55 (35). ISSN 1751-8113

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Official URL: http://dx.doi.org/10.1088/1751-8121/ac8321




Abstract

We investigate the consistency of conditional quantum probabilities. This is whether there is compatibility between the Kolmogorov-Bayes conditional probabilities and the Born rule. We show that they are not compatible in the sense that there are situations where there is no legitimate density matrix that may reproduce the conditional statistics of the other observable via the Born rule. This is to say that the Gleason theorem does not apply to conditional probabilities. Moreover, we show that when this occurs the joint statistics is nonclassical. We show that conditional probabilities are not equivalent to state reduction, so these results do not affect the validity of the Luders expression.


Item Type:Article
Additional Information:

© 2022 IOP Publishing Ltd.
We acknowledge financial support from Spanish Ministerio de Economia y Competitividad Project No. FIS2016-75199-P. We thank Dr G Garcia Moreno for continuous support and helpful comments.

Uncontrolled Keywords:Statistics; Reality; Conditional probabilities; Gleason theorem; Nonclassical states
Subjects:Sciences > Physics > Optics
ID Code:74400
Deposited On:08 Sep 2022 17:55
Last Modified:09 Sep 2022 08:03

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