Infinite-dimensional quantum systems on indefinite causal structures

Flaminia Giacomini, Esteban Castro-Ruiz, Časlav Brukner

Published 2015-10-21Version 1

Standard quantum mechanics assumes that events are embedded in a global causal structure such that, for every pair of events, the causal order between them is always fixed. The process matrix framework keeps the local validity of standard quantum mechanics while relaxing the assumption on the global causal structure. This allows to describe situations in which the order of events is not fixed, i.e. there are processes where it is not possible to specify whether A causes B or B causes A. Such processes are called causally nonseparable. So far, the formalism has been developed only for finite-dimensional systems and a straightforward generalization to infinite dimensions leads to singularities. Here we develop such generalization, and derive the correlations arising from a causally nonseparable process - the quantum switch - in infinite dimensions. The correlations exhibit interference which is due to superposition of processes in which A is before B and B is before A.