The rule of conditional probability is valid in quantum theory [Comment on Gelman & Yao's "Holes in Bayesian Statistics"]

TL;DR

This paper refutes claims that the rules of conditional probability fail in quantum theory, demonstrating that probability rules hold in quantum contexts and are not unique to quantum phenomena.

Contribution

The paper clarifies misconceptions about probability in quantum theory, showing that classical probability rules apply and are not violated in quantum experiments.

Findings

Quantum probability rules are valid in the double-slit experiment.

The quantum inequality discussed also appears in classical non-quantum scenarios.

Misstatements about quantum theory in prior work are corrected.

Abstract

In a recent manuscript, Gelman & Yao (2020) claim that "the usual rules of conditional probability fail in the quantum realm" and that "probability theory isn't true (quantum physics)" and purport to support these statements with the example of a quantum double-slit experiment. The present comment recalls some relevant literature in quantum theory and shows that (i) Gelman & Yao's statements are false; in fact, the quantum example confirms the rules of probability theory; (ii) the particular inequality found in the quantum example can be shown to appear also in very non-quantum examples, such as drawing from an urn; thus there is nothing peculiar to quantum theory in this matter. A couple of wrong or imprecise statements about quantum theory in the cited manuscript are also corrected.