Contextuality and Indistinguishability

TL;DR

This paper explores a quantum-specific approach to contextuality by linking it to indistinguishability, suggesting that indistinguishable yet different properties can resolve traditional contradictions like Kochen-Specker.

Contribution

It introduces a novel perspective connecting quantum contextuality with indistinguishability, offering a potential resolution to classical contextuality paradoxes.

Findings

Indistinguishability allows for consistent property assignment in quantum mechanics.

Repetition of experiments involves measuring indistinguishable but not identical properties.

This approach may help clarify the nature of quantum contextuality.

Abstract

It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities. In this paper we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we assume the ontological thesis that quantum particles or properties can be indistinguishable yet different, no contradiction arising from a Kochen-Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same. We will discuss how the consequences of this move may help us understand quantum contextuality.