Quantum indistinguishability through exchangeable desirable gambles

TL;DR

This paper links the quantum symmetrization postulate to exchangeability assessments of observables, framing quantum indistinguishability as a normative belief update process within a subjective probability perspective.

Contribution

It introduces a novel interpretation of the symmetrization postulate as exchangeability in quantum gambles, connecting quantum theory with subjective probability and belief updating.

Findings

Symmetrization postulate corresponds to exchangeability assessments.

Sets of exchangeable observables can be updated after measurements.

Discusses defining entanglement for indistinguishable particles.

Abstract

Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding systems of identical particles requires a new postulate, the so called symmetrization postulate. In this work, we show that the postulate corresponds to exchangeability assessments for sets of observables (gambles) in a quantum experiment, when quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. Finally, we show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.