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arXiv:2403.07417 · Physical Review A

Cabello's nonlocality argument for multisetting high-dimensional systems and its experimental test

Ming Yang, Dongkai Zhang, Lixiang Chen

Published Jul 15, 2024• 1 citation
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Abstract

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 ($k, d$) 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 $k$ and dimension $d$. 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.

DOI
10.1103/physreva.110.012441

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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.
Characterizing high-dimensional entangled states is of crucial importance in quantum information science and technology. Recent theoretical progress has been made to extend Hardy's paradox into a general scenario with multisetting and multidimensional systems, which enables the maximum probability of nonlocal events to surpass the bound that was limited in Hardy's original test. Hitherto, no experimental verification has been conducted to verify Hardy's paradox, as most of the previous experimental efforts were restricted to two-dimensional systems. Here, based on two-photon high-dimensional orbital angular momentum (OAM) entanglement, we report an experiment to demonstrate Hardy's paradox for multiple settings and multiple outcomes. We demonstrate the paradox for two-setting higher-dimensional OAM subspaces up to d=7d=7d=7, which reveals that the nonlocal events increase with dimension. Furthermore, we showcase the nonlocality with an experimentally recorded probability of 36.77% for a five-setting three-dimensional OAM subspace via entanglement concentration, thus showing a sharper contradiction between quantum mechanics and classical theory.
Characterizing high-dimensional entangled states holds pivotal significance in quantum information science and technology. Recent theoretical progress has been made to extend the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality into a general scenario with multisetting and multidimensional systems. Here, by employing two-photon orbital angular momentum entanglement, we conduct an experiment to demonstrate the CGLMP inequality across multiple settings and outcomes. Our experimental results violate the CGLMP inequality by more than 12 standard deviations, demonstrating that the maximum violation increases with both dimension and setting. Furthermore, we reveal, both theoretically and experimentally, the logical connection between the CGLMP inequality and the general Hardy's paradox. Intriguingly, our analysis establishes that, even in high-dimensional systems, Hardy's paradox can be regarded as a special instance of Bell inequality, with their respective bounds aligning under the no-signaling principle and the information causality principle. Our work may advance the foundational understanding of quantum correlations in high-dimensional quantum systems.
In this paper, we study the Hardy nonlocal argument (HNA) and the Cabello nonlocal argument (CNA) under the Information Causality, Macroscopic Locality and Local Orthogonality principles in the context of Local Randomness. We see that, in the context of all the possibilities of local randomness, the gap between the quantum mechanics and the above principles, in the Cabello's nonlocality argument is larger than the Hardy's case. Therefore the CNA is stronger control than the HNA for detecting post-quantum nosignalling correlations.
Recently, an alternative form of Hardy's paradox was introduced for two-setting high-dimensional systems [Phys. Rev. A 88, 062116 (2013)], for which the maximum probability of the nonlocal event was shown to increase as the dimension goes larger. Here, we generalize the result to a general scenario with multisetting high-dimensional systems. The general Hardy's paradox (i) reduces to the one by Chen et al. [Phys. Rev. A 88, 062116 (2013)] for two settings, (ii) is equivalent to the ladder proof of nonlocality without inequalities given by Boschi et al. [Phys. Rev. Lett. 79, 2755 (1997)] for two-dimensional systems, and (iii) increases the maximum probability of the nonlocal event for, e.g., three-dimensional systems. In particular, the maximum probability for the five-setting three-dimensional system is increased to 0.401840.401\phantom{\rule{0.16em}{0ex}}840.40184, which is larger than 0.171 originally by Cabello [Phys. Rev. A 58, 1687 (1998)].
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.
Hardy-type arguments manifest Bell nonlocality in one of the simplest possible ways. Except for demonstrating nonclassical signature of entangled states in question, they can also serve for device-independent self-testing of states, as shown, e.g., in Phys. Rev. Lett. 109, 180401 (2012). Here we develop and broaden these results to an extended version of Hardy's argument, often referred to as Cabello's nonlocality argument. We show that, as in the simpler case of Hardy's nonlocality argument, the maximum quantum value for Cabello's nonlocality is achieved by a pure two-qubit state and projective measurements that are unique up to local isometries. We also examine the properties of a more realistic case when small errors in the ideal constraints are accepted within the probabilities obtained and prove that also in this case the two-qubit state and measurements are sufficient for obtaining the maximum quantum violation of the classical bound.