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arXiv:2403.09220 · Optics Express

Demonstration of universal contextuality through communication games free of both operational inequivalence and compatibility loopholes

Xuan Fan, Xiao Ya, Yongjian Gu

Published Nov 20, 2023• 1 citation
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Abstract

Universal contextuality is the leading notion of non-classicality even for single systems, showing its advantage as a more general quantum correlation than Bell non-locality, as well as preparation contextuality. However, a loophole-free experimental demonstration of universal contextuality at least requires that both operational inequivalence and compatibility loopholes are closed, which have never been simultaneously achieved to date. In our work, we experimentally test universal contextuality through (3,3) and (4,3) communication games, simultaneously restoring operational equivalence and circumventing the compatibility loophole. Our result exhibits the violation of universal non-contextuality bound by 97 standard deviations in (3,3) scenario, and 107 deviations in (4,3) scenario. Notably there are states which exhibit locality but reveal universal contextuality in both two scenarios. In addition, our result shows that universal contextuality is more general than preparation contextuality in (3,3) scenario, while equivalent to preparation contextuality in (4,3) scenario.

DOI
10.1364/oe.502723

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Universal contextuality is the leading notion of non-classicality even for single systems, showing its advantage as a more general quantum correlation than Bell non-locality, as well as preparation contextuality. However, a loophole-free experimental demonstration of universal contextuality at least requires that both operational inequivalence and compatibility loopholes are closed, which have never been simultaneously achieved to date. In our work, we experimentally test universal contextuality through (3,3) and (4,3) communication games, simultaneously restoring operational equivalence and circumventing the compatibility loophole. Our result exhibits the violation of universal non-contextuality bound by 97 standard deviations in (3,3) scenario, and 107 deviations in (4,3) scenario. Notably there are states which exhibit locality but reveal universal contextuality in both two scenarios. In addition, our result shows that universal contextuality is more general than preparation contextuality in (3,3) scenario, while equivalent to preparation contextuality in (4,3) scenario.
Universal contextuality is the leading notion of non-classicality even for single systems, showing its advantage as a more general quantum correlation than Bell non-locality, as well as preparation contextuality. However, a loophole-free experimental demonstration of universal contextuality at least requires that both operational inequivalence and compatibility loopholes are closed, which have never been simultaneously achieved to date. In our work, we experimentally test universal contextuality through (3,3) and (4,3) communication games, simultaneously restoring operational equivalence and circumventing the compatibility loophole. Our result exhibits the violation of universal non-contextuality bound by 97 standard deviations in (3,3) scenario, and 107 deviations in (4,3) scenario. Notably there are states which exhibit locality but reveal universal contextuality in both two scenarios. In addition, our result shows that universal contextuality is more general than preparation contextuality in (3,3) scenario, while equivalent to preparation contextuality in (4,3) scenario.
An ontological model of an operational theory is considered to be universally noncontextual if both preparation and measurement noncontextuality assumptions are satisfied in that model. In this report, we first generalize the logical proofs of quantum preparation and measurement contextuality for qubit system for any odd number of preparations and measurements. Based on the logical proof, we derive testable universally non-contextual inequalities violated by quantum theory. We then propose a class of two-party communication games and show that the average success probability of winning such games is solely linked to suitable Bell expression whose local bound is greater than universal non-contextual bound. Thus, for a given state, even if quantum theory does not exhibit non-locality, it may still reveal non-classicality by violating the universal non-contextual bound. Further, we consider a different communication game to demonstrate that for a given choices of observables in quantum theory, even if there is no logical proof of preparation and measurement contextuality exist, the universal quantum contextuality can be revealed through that communication game. Such a game thus test a weaker form of universal non-contextuality with minimal assumption.
We investigate discriminability from an operational and contextuality-oriented perspective using a two-copy comparison game based on SWAP-type measurements. The resulting score DopD_{\mathrm{op}}Dop​ provides an experimentally accessible notion of distinguishability that does not rely on a minimum-error discrimination task. We first examine whether this discriminability game can directly witness preparation contextuality. Within a preparation-noncontextual ontological model, we derive a direct upper bound on the game score under a SWAP-like comparison rule and a sharp single-copy test, and show that this bound is saturated in the natural qubit realization. Thus, the direct game alone does not provide a contextuality witness in that regime. We then consider a Bell-coupled scenario in which two-copy comparison measurements are applied to Bob's conditional preparations. This yields a state-dependent upper bound on the CHSH value in terms of operational separation parameters, and hence in terms of the distinguishability of the conditional states. Our results establish a quantitative link between operational discriminability and the strength of nonclassical correlations, showing that discriminability can act as an operational resource constraining Bell-type nonclassical correlations.
Bell non-locality is a fundamental feature of quantum mechanics whereby measurements performed on “spatially separated” quantum systems can exhibit correlations that cannot be understood as revealing predetermined values. This is a special case of the more general phenomenon of “quantum contextuality”, which says that such correlations can occur even when the measurements are not necessarily on separate quantum systems, but are merely “compatible” (i.e. commuting). Crucially, while any non-local game yields an experiment that demonstrates quantum advantage by leveraging the “spatial separation” of two or more devices (and in fact several such demonstrations have been conducted successfully in recent years), the same is not true for quantum contextuality: finding the contextuality analogue of such an experiment is arguably one of the central open questions in the foundations of quantum mechanics. In this work, we show that an arbitrary contextuality game can be compiled into an “operational test of contextuality” involving a single quantum device, by only making the assumption that the device is computationally bounded. Our work is inspired by the recent work of Kalai et al. (STOC '23) that converts any non-local game into a classical test of quantum advantage with a single device. The central idea in their work is to use cryptography to enforce spatial separation within subsystems of a single quantum device. Our work can be seen as using cryptography to enforce “temporal separation”, i.e. to restrict communication between sequential measurements. Beyond contextuality, we employ our ideas to design a “proof of quantumness” that, to the best of our knowledge, is arguably even simpler than the ones proposed in the literature so far.
Communication games are collaborative information processing tasks involving a number of players with limited communication. Such games are useful tools for studying physical theories. A physical theory exhibits preparation contextuality whenever observed behaviour cannot be explained by a preparation noncontextual model. Here we show that there is a fundamental connection between the performance in communication games and the degree of preparation (non)contextuality. For this purpose, we present a general framework that allows us to construct communication games such that the game performance corresponds to a measure of preparation (non)contextuality. We illustrate the power of this framework by, 1) deriving many examples of tests of preparation contextuality, 2) showing that quantum violations of Bell inequalities can be derived from quantum violations of preparation noncontextuality, 3) qualitatively and quantitatively explaining related previous results on preparation contextuality in quantum communication games, and 4) solving the open problem of revealing the preparation contextuality of the maximally mixed quantum state in any dimension.
Conventional wisdom asserts that measurement incompatibility is necessary for revealing the non-locality and contextuality. In contrast, a recent work [Phys. Rev. Lett. 130, 230201 (2023)] demonstrates the generalized contextuality without measurement incompatibility by using a five-outcome qubit measurement. In this paper, we introduce a two-party prepare-measure communication game involving specific constraints on preparations, and we demonstrate contextuality sans incompatibility in the simplest measurement scenario, requiring only a three-outcome extremal qubit measurement. This contrasts with the aforementioned five-outcome qubit measurement, which can be simulated by an appropriate convex mixture of five three-outcome incompatible qubit measurements. Furthermore, we illustrate that our result has a prominent implication in information theory. Our communication game can be perceived as a constrained Holevo-Frankle-Weiner (HFW) scenario, as operational restrictions are imposed on preparations. We show that the maximum success probability of the game by using a qubit surpasses that attainable by a c-bit, even when shared randomness is a free resource. Consequently, this finding exemplifies the supremacy of a qubit over a c-bit within a constrained HFW framework. Thus, alongside offering fresh insights into quantum foundations, our results pave a novel pathway for exploring the efficacy of a qubit in information processing tasks.