Indistinguishability and Negative Probabilities

TL;DR

This paper explores how quantum indistinguishability relates to negative probabilities and no-signaling, introducing a measure-theoretic approach to signed probabilities inspired by quantum contextuality.

Contribution

It provides a measure-theoretic framework linking quantum indistinguishability, negative probabilities, and no-signaling conditions, advancing understanding of quantum contextuality.

Findings

Indistinguishability implies no-signaling

Signed probabilities can be formalized measure-theoretically

Negative probabilities relate to quantum contextuality

Abstract

In this paper, we examined the connection between quantum systems' indistinguishability and signed (or negative) probabilities. We do so by first introducing a measure-theoretic definition of signed probabilities inspired by research in quantum contextuality. We then argue that ontological indistinguishability leads to the no-signaling condition and negative probabilities.