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.
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.
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.
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.
The Kochen–Specker (KS) theorem reveals the nonclassicality of single quantum systems. In contrast, Bell's theorem and entanglement concern the nonclassicality of composite quantum systems. Accordingly, unlike incompatibility, entanglement and Bell non-locality are not necessary to demonstrate KS-contextuality. However, here we find that for multiqubit systems, entanglement and non-locality are both essential to proofs of the Kochen–Specker theorem. Firstly, we show that unentangled measurements (a strict superset of local measurements) can never yield a logical (state-independent) proof of the KS theorem for multiqubit systems. In particular, unentangled but nonlocal measurements—whose eigenstates exhibit ''nonlocality without entanglement"—are insufficient for such proofs. This also implies that proving Gleason's theorem on a multiqubit system necessarily requires entangled projections, as shown by Wallach [Contemp Math, 305: 291-298 (2002)]. Secondly, we show that a multiqubit state admits a statistical (state-dependent) proof of the KS theorem if and only if it can violate a Bell inequality with projective measurements. We also establish the relationship between entanglement and the theorems of Kochen–Specker and Gleason more generally in multiqudit systems by constructing new examples of KS sets. Finally, we discuss how our results shed new light on the role of multiqubit contextuality as a resource within the paradigm of quantum computation with state injection.
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for some realistic models with hidden variables. There are, however, two powerful theorems against the hidden-variable theories showing that certain quantum features cannot be reproduced based on two rationale premises of classicality, the Bell theorem, and noncontextuality, due to Bell, Kochen and Specker (BKS) . Tests of the Bell inequality and the BKS theorem are both of fundamental interests and of great significance . The Bell theorem has already been experimentally verified extensively on many different systems , while the quantum contextuality, which is independent of nonlocality and manifests itself even in a single object, is experimentally more demanding. Moreover, the contextuality has been shown to play a critical role to supply the `magic' for quantum computation, making more extensive experimental verifications in potential systems for quantum computing even more stringent. Here we report an experimental verification of quantum contextuality on an individual atomic nuclear spin-1 system in solids under ambient condition. Such a three-level system is indivisible and thus the compatibility loophole, which exists in the experiments performed on bipartite systems, is closed. Our experimental results confirm that the quantum contextuality cannot be explained by nonlocal entanglement, revealing the fundamental quantumness other than locality/nonlocality within the intrinsic spin freedom of a concrete natural atomic solid-state system at room temperature.
Abstract The relations between Bell nonlocality and Kochen–Specker contextuality have been subject of research from many different perspectives in the last decades. Recently, some interesting results on these relations have been explored in the so-called generalized Bell scenarios, that is, scenarios where Bell spatial separation (or agency independence) coexist with (at least one of the) parties’ ability to perform compatible measurements at each round of the experiment. When this party has an n-cycle compatiblity setup, it was first claimed that Bell nonlocality could not be concomitantly observed with contextuality at this party’s local experiment. However, by a more natural reading of the definition of locality, it turns out that both Bell nonlocality and local contextuality can, in fact, be jointly present. In spite of it, in this work we prove that in the simplest of those scenarios there cannot be arbitrary amounts of both of these two resources together. That is, in these cases we show that the violation of any Bell inequality limits the possible violations of any local noncontextuality inequality. We also explore this trade-off relation using quantifiers of nonlocality and contextuality, discussing how such a relation can be understood in terms of a ‘global’ notion of contextuality, and we study possible extensions of this result to other scenarios.
Contextuality provides one of the fundamental characterizations of quantum phenomena, and can be used as a resource in lots of quantum information processing. In this paper, we summarize and derive some equivalent noncontextual inequalities from different noncontextual models of the proofs for the Kochen-Specker theorem based on Greenberger-Horne-Zeilinger states. These noncontextual inequalities are equivalent up to some correlation items which hold both for noncontextual hidden variable theories and quantum mechanics. Therefore, using single-photon hyperentangled Greenberger-Horne-Zeilinger states encoded by spin, path, and orbital angular momentum, we experimentally verify several state-dependent noncontextual models of the proofs for the Kochen-Specker theorem by testing an extreme simplest Mermin-like inequality.