Allen, J-MA;
Barrett, J;
Horsman, DC;
Lee, CM;
Spekkens, RW;
(2017)
Quantum Common Causes and Quantum Causal Models.
Physical Review X
, 7
(3)
, Article 031021. 10.1103/PhysRevX.7.031021.
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Abstract
Reichenbach’s principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional probability distribution over the variables given the complete common cause should factorize. The principle is generalized by the formalism of causal models, in which the causal relationships among variables constrain the form of their joint probability distribution. In the quantum case, however, the observed correlations in Bell experiments cannot be explained in the manner Reichenbach’s principle would seem to demand. Motivated by this, we introduce a quantum counterpart to the principle. We demonstrate that under the assumption that quantum dynamics is fundamentally unitary, if a quantum channel with input A and outputs B and C is compatible with A being a complete common cause of B and C , then it must factorize in a particular way. Finally, we show how to generalize our quantum version of Reichenbach’s principle to a formalism for quantum causal models and provide examples of how the formalism works.
| Type: | Article |
|---|---|
| Title: | Quantum Common Causes and Quantum Causal Models |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1103/PhysRevX.7.031021 |
| Publisher version: | https://doi.org/10.1103/PhysRevX.7.031021 |
| Language: | English |
| Additional information: | Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. |
| Keywords: | Science & Technology, Physical Sciences, Physics, Multidisciplinary, Physics, Bell-Inequality, Formulation, Operations, Principle, Equality, Entropy |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1571859 |
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