Born Rule and Logical Inference in Quantum Mechanics

TL;DR

This paper extends the logical interpretation of probability to quantum mechanics, deriving the Born rule by applying logical inference to commuting projectors, thus viewing quantum mechanics as an extension of classical probability.

Contribution

It provides a novel derivation of the Born rule based on logical inference principles within the framework of quantum mechanics.

Findings

Derivation of the Born rule from logical inference

Quantum mechanics viewed as an extension of classical probability

Logical interpretation applied to quantum propositions

Abstract

Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this paper, assuming that our usual inference procedure makes sense for every set of logical propositions represented in terms of commuting projectors on a given Hilbert space, we extend the logical interpretation to quantum mechanics and derive the Born rule. Our result implies that, from the epistemological viewpoints, we can regard quantum mechanics as a natural extension of the classical probability.