Superluminal signalling witness for quantum state reduction

TL;DR

This paper introduces a universal witness for superluminal signalling in quantum state reduction models, revealing that many known models may permit faster-than-light communication unless specific locality conditions are met.

Contribution

It formulates a general superluminal signalling witness applicable to complex models with correlated noise, providing a necessary and sufficient condition to exclude superluminal signals.

Findings

Linear master equations may still allow superluminal signalling.

The witness is effective for models with correlated noise.

Some models can avoid superluminal signalling by satisfying locality conditions.

Abstract

Models for quantum state reduction address the quantum measurement problem by suggesting weak modifications to Schr\"odinger's equation that have no observable effect at microscopic scales, but dominate the dynamics of macroscopic objects. Enforcing linearity of the master equation for such models has long been used as a way of ensuring that modifications to Schr\"odinger's equation do not introduce a possibility for superluminal signalling. In large classes of quantum state reduction models, however, and in particular in models employing correlated noise, formulating a master equation for the quantum state is prohibitively difficult or impossible. Here, we formulate a witness for superluminal signalling that is applicable to generic quantum state reduction models, including those involving correlated as well as uncorrelated noise. Surprisingly, application of the witness to known models described by linear master equations shows that these may still admit superluminal signalling, unless a particular locality condition is obeyed. In contrast, we show that the witness introduced here provides a necessary and sufficient condition for excluding superluminal signals under all circumstances. We further apply the witness to several models driven by physical, correlated noise, where linear master equations are not analytically obtainable, and find that they allow for superluminal signalling. We suggest how specific correlated-noise models may be able to avoid it, and that the witness introduced here provides a stringent guide to constructing such models.