On the Interpretation of Quantum Indistinguishability : a No-Go Theorem

TL;DR

This paper presents a no-go theorem demonstrating that realist interpretations of quantum indistinguishability, based on overlaps of probability distributions, cannot reproduce certain quantum predictions like maximal Mermin inequality violations.

Contribution

It proves that all ontological models explaining quantum indistinguishability via distribution overlaps are incompatible with quantum predictions, challenging realist interpretations.

Findings

Maximal violation of Mermin inequality cannot be explained by overlap-based ontological models.

Realist interpretations based on probability overlaps are incompatible with quantum mechanics.

The result constrains possible interpretations of quantum indistinguishability.

Abstract

Despite being the most fundamental object in quantum theory, physicists are yet to reach a consensus on the interpretation of a quantum wavefunction. In the broad class of realist approaches, quantum states are viewed as Liouville-like probability distributions over some space of physical variables where indistinguishabity of non-orthogonal states is attributed to overlaps between these distributions. Here we argue that such an interpretation of quantum indistinguishability is wrong. In particular, we show that quantum mechanical prediction of maximal violation of Mermin inequality in certain thought experiment is incompatible with all ontological interpretations for quantum theory where indistinguishability of non-orthonal quantum states is explained, even partially, in terms of overlap of their Liouville distributions.