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Physical Review Letters

Orbital Angular Momentum Experiment Converting Contextuality into Nonlocality

Jianqi Sheng, Dongkai Zhang, Lixiang Chen

Published Jan 3, 2025• 4 citations
Publisher

Abstract

It was recently revealed by Cabello in a theoretical Letter [Phys. Rev. Lett. 127, 070401 (2021)PRLTAO0031-900710.1103/PhysRevLett.127.070401] that nonlocality and contextuality, as two intuitively distinctive yet both critical quantum resources, can be surprisingly connected through Bell inequalities associated with state-independent contextuality sets. It provides a general unified method capable of converting contextuality into bipartite nonlocality. However, experimental tests of the inequalities are challenging and noise sensitive, and the requirements for the quantum states purity, dimensionality, and degree of entanglement have blocked the experimental implementation. We report a first experimental test of Cabello's inequalities from state-independent contextuality sets, by leveraging two-photon high-dimensional orbital angular momentum entangled states. Distinguishing from the standard single-particle ways, our experiment spotlights that the state-independent contextuality sets can be tested in a bipartite scenario, by which the "compatibility" or "sharpness" loopholes can be effectively avoided. Our results provide a new perspective and demonstrate the principle that contextuality, a widely used quantum resource, can be used in different physical scenarios.

DOI
10.1103/physrevlett.134.010203

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It was recently revealed by Cabello in a theoretical Letter [Phys. Rev. Lett. 127, 070401 (2021)PRLTAO0031-900710.1103/PhysRevLett.127.070401] that nonlocality and contextuality, as two intuitively distinctive yet both critical quantum resources, can be surprisingly connected through Bell inequalities associated with state-independent contextuality sets. It provides a general unified method capable of converting contextuality into bipartite nonlocality. However, experimental tests of the inequalities are challenging and noise sensitive, and the requirements for the quantum states purity, dimensionality, and degree of entanglement have blocked the experimental implementation. We report a first experimental test of Cabello's inequalities from state-independent contextuality sets, by leveraging two-photon high-dimensional orbital angular momentum entangled states. Distinguishing from the standard single-particle ways, our experiment spotlights that the state-independent contextuality sets can be tested in a bipartite scenario, by which the "compatibility" or "sharpness" loopholes can be effectively avoided. Our results provide a new perspective and demonstrate the principle that contextuality, a widely used quantum resource, can be used in different physical scenarios.
There are two powerful arguments against the possibility of extending quantum mechanics, the violation of Bell inequalities and the Kochen-Specker theorem, but the connection between the two remains confused. Following the distinctive strategy proposed by Cabello [Phys. Rev. Lett. 127, 070401 (2021)], Bell inequalities can be violated by state-independent contextuality sets. However, the experimental realization of such ideas is challenging as it requires high-dimensional entanglement. Orbital angular momentum provides an unlimited state space and the number of effective dimensions can be readily tailored as required. We performed an experimental test of non-locality based on Bell inequalities from contextuality, using orbital angular momentum entanglement in a bipartite photonic system. Our experiment not only shows a new way to produce non-locality but also connects contextuality and non-locality, two fundamental quantum resources that are critical for quantum computation and secure communication tasks.
Recent advancements have expanded Hardy's nonlocality arguments into multisetting and multidimensional systems to enhance quantum correlations. In comparison with Hardy's nonlocality argument, Cabello's nonlocality argument (CNA) emerges as a superior choice for illustrating nonlocal features. An open question persists regarding the potential extension of CNA to arbitrary (k,dk, dk,d) scenarios. Here, we answer this question both in theory and experiment. Theoretically, by utilizing compatibility graphs, we construct a new logical framework for multisetting and multidimensional CNA, demonstrating an increase in the maximum successful probability with setting kkk and dimension ddd. Experimentally, by employing controllable photonic orbital angular momentum entanglement, we exhibit nonlocality with an experimentally recorded probability of 20.29% in the (2, 4) scenario and 28.72% in the (6, 2) scenario. Our work showcases a sharper contradiction between quantum mechanics and classical theory, surpassing the bound limited by the original version.
Bell nonlocality and quantum contextuality are two important resources which, however, behave very differently in many tasks where the quantum correlation has an edge over its classical counterpart. In this work, we directly compare these two behaviors, which via the Cabello-Severini-Winter graph-theoretical approach, can be associated with a same exclusivity graph. In particular, we consider the exclusivity graph that leads to I3322{I}_{3322}I3322​-type inequalities in the Bell and the contextual scenarios, respectively. We find that maximal violation of Bell inequality is around 6.251, and maximal violation of the noncontextuality inequality is around 6.588 for a five-dimensional system and 6.571 for a four-dimensional system, respectively. The results predict a gap of $\mathrm{\ensuremath{\Delta}}\ensuremath{\approx}0.32$ between quantum contextuality and Bell nonlocality. We then present an experimental observation of the gap by employing both the maximally entangled photon pairs from the spontaneous parametric down-conversion process and the single photons encoded into qudits from an intrinsic defect in gallium nitride. Our results will further deepen the understanding of different types of quantum correlations.
The physical impact and the testability of the Kochen-Specker (KS) theorem is debated because of the fact that perfect compatibility in a single quantum system cannot be achieved in practical experiments with finite precision. Here, we follow the proposal of A. Cabello and M. T. Cunha [Phys. Rev. Lett. 106, 190401 (2011)], and present a compatibility-loophole-free experimental violation of an inequality of noncontextual theories by two spatially separated entangled qutrits. A maximally entangled qutrit-qutrit state with a fidelity as high as 0.975±0.001 is prepared and distributed to separated spaces, and these two photons are then measured locally, providing the compatibility requirement. The results show that the inequality for noncontextual theory is violated by 31 standard deviations. Our experiments pave the way to close the debate about the testability of the KS theorem. In addition, the method to generate high-fidelity and high-dimension entangled states will provide significant advantages in high-dimension quantum encoding and quantum communication.
Contextuality is a distinctive feature of quantum theory and a fundamental resource for quantum computation. However, existing examples of contextuality in high-dimensional systems lack the necessary robustness required in experiments. Here, we address this problem by identifying a family of noncontextuality inequalities whose maximum quantum violation grows with the dimension of the system. At first glance, this contextuality is the single-system version of multipartite Bell nonlocality taken to an extreme form. What is interesting is that the single-system version achieves the same degree of contextuality but uses a Hilbert space of lower dimension. That is, contextuality "concentrates" as the degree of contextuality per dimension increases. We show the practicality of this result by presenting an experimental test of contextuality in a seven-dimensional system. By simulating sequences of quantum ideal measurements with destructive measurements and repreparation in an all-optical setup, we report a violation of 68.7 standard deviations of the simplest case of the noncontextuality inequalities identified. Our results advance the investigation of high-dimensional contextuality, its connection to the Clifford algebra, and its role in quantum computation.
We experimentally show that nonlocality can be produced from single-particle contextuality by using two-particle correlations which do not violate any Bell inequality by themselves. This demonstrates that nonlocality can come from an a priori different simpler phenomenon, and connects contextuality and nonlocality, the two critical resources for, respectively, quantum computation and secure communication. From the perspective of quantum information, our experiment constitutes a proof of principle that quantum systems can be used simultaneously for both quantum computation and secure communication.