Non-Commutation Chains in Pre- and Post-Selection Paradoxes

Abstract

Peculiar measurements can be obtained on systems that undergo both pre- and post-selection. We prove a conjecture from [1] on logical Pre- and Post-Selection (PPS) paradoxes for a restricted case. We prove that all of these paradoxes admit non-commutation chains. We also relate this to the theory of causal balance, recently introduced in [1], and show how the theory blocks such paradoxes.