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Quantum causal models via quantum Bayesianism

Phys. Rev. A 101, 012104 – Published 8 January 2020
Pienaar, J. International Institute of Physics (Universidade Federal do Rio Grande do Norte) 2020 Physics

This paper presents a framework for quantum causal modeling based on the interpretation of causality as a relation between an observer's probability assignments to hypothetical or counterfactual experiments. The framework is based on the principle of “causal sufficiency”: that it should be possible to make inferences about interventions using only the probabilities from a single “reference experiment” plus causal structure in the form of a directed acyclic graph. This leads to several interesting results: we find that quantum measurements deserve a special status distinct from interventions, and that a special rule is needed for making inferences about what would happen if they are not performed (“unmeasurements”). One natural candidate for this rule is found to be an equation of importance to the quantum Bayesianism interpretation of quantum mechanics. We find that the causal structure of quantum systems must have a “layered” structure, and that the model can naturally be made symmetric under reversal of the causal arrows.

The article was published in: Phys. Rev. A 101, 012104 – Published 8 January 2020

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This work was supported (in part) by the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust.