Frame dependence of Spekkens' contextuality for relativistic spin systems

Abstract

We show that the operational definition of contextuality introduced by Spekkens is, in general, not Lorentz invariant. Specifically, we consider an explicit example with particle states consisting of both spin and momentum, we apply a Lorentz transformation to obtain the states in a new inertial frame, and then trace out the momentum degrees of freedom in both frames. We find that, while an observer in the first inertial frame describes a contextual ontological model with respect to spin states and all possible spin measurements, an observer in the boosted frame describes a non-contextual model with respect to the transformed spin states and all transformed spin measurements. Hence, the Spekkens' notion of contextuality, when restricted to spin degress of freedom only, is a frame-dependent concept. We apply our results to predict a novel relativistic effect concerning the task of discriminating between two quantum states. We show that the probability of success for a moving observer exceeds that of an observer at rest.