Certified Quantumness via Single-Shot Temporal Measurements

• URL: http://arxiv.org/abs/2206.02581v3
• Date: Sat, 05 Oct 2024 16:33:33 GMT
• Title: Certified Quantumness via Single-Shot Temporal Measurements
• Authors: Md Manirul Ali, Sovik Roy,
• Abstract summary: Bell-Kochen-Specker theorem states that a non-contextual hidden- variable theory cannot reproduce predictions of quantum mechanics. Asher Peres gave a simple proof of quantum contextuality in a four-dimensional Hilbert space of two spin-1/2 particles. We present a similar proof in time with a temporal version of the Peres-like argument.
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• Abstract: Bell-Kochen-Specker theorem states that a non-contextual hidden-variable theory cannot completely reproduce the predictions of quantum mechanics. Asher Peres gave a remarkably simple proof of quantum contextuality in a four-dimensional Hilbert space of two spin-1/2 particles. Peres's argument is enormously simpler than that of Kochen and Specker. Peres contextuality demonstrates a logical contradiction between quantum mechanics and the noncontextual hidden variable models by showing an inconsistency when assigning noncontextual definite values to a certain set of quantum observables. In this work, we present a similar proof in time with a temporal version of the Peres-like argument. In analogy with the two-particle version of Peres's argument in the context of spin measurements at two different locations, we examine here single-particle spin measurements at two different times $t=t_1$ and $t=t_2$. We adopt three classical assumptions for time-separated measurements, which are demonstrated to conflict with quantum mechanical predictions. Consequently, we provide a non-probabilistic proof of certified quantumness in time, without relying on inequalities, demonstrating that our approach can certify the quantumness of a device through single-shot, time-separated measurements. Our results can be experimentally verified with the present quantum technology.

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