Quantum mechanics does not allow violation of the pigeon counting principle

Abstract

Aharonov et al. (2016) argued that the pigeonhole counting principle (PCP) is violated in quantum mechanics and maintains this position in their comment. While statements (i) and (ii) in the comment are correct, to reach the conclusion of PCP violation requires more than this — the assignment of specific values to a set of commuting operators. We reiterate that their conclusion is incorrect because the assigned values are inconsistent with an operator identity imposed by quantum mechanics. We then use the consistent histories approach to quantum mechanics to show where the arguments of Aharonov et al. break down.