Violation of no signaling in higher order quantum measure theories

TL;DR

This paper investigates higher-order quantum measure theories and demonstrates that violating certain sum-rules can enable superluminal signaling, raising questions about fundamental physical principles.

Contribution

It shows that under specific assumptions, violating higher-order sum-rules in quantum measure theories can lead to superluminal communication, linking mathematical structure to physical causality.

Findings

Violation of higher sum-rules permits superluminal signaling

Quantum measure theories extend classical probability sum-rules

Physical principles may forbid certain sum-rule violations

Abstract

More general probability sum-rules for describing interference than 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 under certain assumptions, violation of higher sum-rules allows for superluminal signaling.