Variable-strength non-local measurements reveal quantum violations of classical counting principles

TL;DR

This paper demonstrates quantum violations of classical counting principles using variable-strength non-local measurements, revealing persistent violations of the pigeonhole principle even under weak measurement conditions.

Contribution

It introduces the first variable-strength measurement of a non-local observable to explore quantum violations of classical counting rules.

Findings

Violations of the pigeonhole principle are observed even with weak measurements.

The sum rule violation decreases as measurement strength decreases.

Cancellation of imaginary parts in weak values restores the sum rule in the weak limit.

Abstract

We implement a variant of the quantum pigeonhole paradox thought experiment to study whether classical counting principles survive in the quantum domain. We observe strong measurements significantly violate the pigeonhole principle (that among three pigeons in two holes, at least one pair must be in the same hole) and the sum rule (that the number of pigeon pairs in the same hole is the sum of the number of pairs across each of the holes) in an ensemble that is pre and postselected into particular separable states. To investigate whether measurement disturbance is a viable explanation for these counter-intuitive phenomena, we employ the first ever variable-strength measurement of a non-local observable. As we decrease the measurement strength, we find the violation of the sum rule decreases, yet the pigeonhole principle remains violated. In the weak limit, the sum rule is restored due to the cancellation between two weak values with equal and opposite imaginary parts. We observe the same kind of cancellation at higher measurement strengths, thus raising the question: do strong measurements have imaginary parts?