Coherence as a resource for $N$-box and quantum pigeonhole paradoxes

• URL: http://arxiv.org/abs/2607.24282v1
• Date: Mon, 27 Jul 2026 11:29:15 GMT
• Title: Coherence as a resource for $N$-box and quantum pigeonhole paradoxes
• Abstract summary: We show that two such scenarios, the $N$-box and quantum pigeonhole paradoxes, require coherence of both pre- and post-selected states.<n>This is done by showing each paradox holds if and only if there is weak-value anomaly for a single, paradox-specific operator.
• Score: 0.1529342790344802
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Pre- and post-selection (PPS) paradoxes are striking demonstrations of quantum nonclassicality. Logical PPS paradoxes, where inferences made with the Aharonov-Bergmann-Lebowitz (ABL) rule are exactly 0 or 1, are linked to contextuality. Non-logical paradoxes lack this strong signature. In this work, we analyse more general, non-logical PPS scenarios involving mixed pre- and post-selected states. We show that two such scenarios, the $N$-box and quantum pigeonhole paradoxes, require coherence of both pre- and post-selected states in the basis of the intermediate measurement. This is done by showing each paradox holds if and only if there is weak-value anomaly for a single, paradox-specific operator, together with the fact that weak-value anomaly requires coherence. This clarifies the role of different notions of nonclassicality in these scenarios, highlighting the required quantitative departures from (strictly) classical explanations provided by incoherent sub-theories of quantum theory.

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