  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.
