Superluminal signalling witness for quantum state reduction

Models for quantum state reduction address the quantum measurement problem by suggesting weak modifications to Schrödinger'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 Schrödinger'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.