Violation of no-signaling in higher-order quantum measure theories

Abstract

More general probability sum-rules for describing interference found in quantum mechanics (QM) were formulated by Sorkin in a hierarchy of such rules. The additivity of classical measure theory corresponds to the second sum-rule. QM violates this rule, but satisfies the third and higher sum-rules. This evokes the question of whether there are physical principles that forbid their violation. We show that in a theory that is indistinguishable from quantum mechanics in first and second-order interferences, the violation of higher sum-rules allows for superluminal signaling, essentially because probability measures can be contextual in such theories.