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More general probability sum-rules for describing interference than found inquantum 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. Thisevokes the question of whether there are physical principles that forbid theirviolation. We show that under certain assumptions, violation of highersum-rules allows for superluminal signaling.

Violation of no signaling in higher order quantum measure theories