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arXiv:2503.14587

Quantum contextuality of spin-1 massive particles

Marco E. Fabbrichesi, Roberto Floreanini B, Emidio Gabrielli A, Luca Marzola

Published Mar 18, 2025• 0 citations
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Abstract

Contextuality is a fundamental property of quantum mechanics. Contrary to entanglement, which can only exist in composite systems, contextuality is also present for single entities. The case of a three-level system is of particular interest because--in agreement with the Bell-Kochen-Specker theorem--it is the simplest in which quantum contextuality is necessarily present. We verify that the polarizations of spin-1 massive particles produced at collider experiments indeed exhibit contextuality. To this purpose we consider $W$ gauge bosons produced in top-quark decays, $J/ψ$ and $K^{*}(892)^0$ mesons created in $B$-meson decays and $ϕ$ mesons resulting from $χ^0_c$ charmonium decays, making use of the data collected and analyzed by the ATLAS, LHCb and BESIII collaborations, respectively. The polarizations of all these four particles show contextuality with a significance of more than $5σ$.

DOI
10.48550/arxiv.2503.14587

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Contextuality is a fundamental property of quantum mechanics. Contrary to entanglement, which can only exist in composite systems, contextuality is also present for single entities. The case of a three-level system is of particular interest because--in agreement with the Bell-Kochen-Specker theorem--it is the simplest in which quantum contextuality is necessarily present. We verify that the polarizations of spin-1 massive particles produced at collider experiments indeed exhibit contextuality. To this purpose we consider WWW gauge bosons produced in top-quark decays, J/ψJ/ψJ/ψ and K∗(892)0K^{*}(892)^0K∗(892)0 mesons created in BBB-meson decays and ϕϕϕ mesons resulting from χc0χ^0_cχc0​ charmonium decays, making use of the data collected and analyzed by the ATLAS, LHCb and BESIII collaborations, respectively. The polarizations of all these four particles show contextuality with a significance of more than 5σ5σ5σ.
Quantum contextuality refers to the impossibility of assigning a predefined, intrinsic value to a physical property of a system independently of the context in which the property is measured. It is, perhaps, the most fundamental feature of quantum mechanics. The many states with different spin that particle physics provides are the ideal setting for testing contextuality. We verify that the polarization states of single spin-1 massive particles produced at colliders are contextual. We test W + gauge bosons produced in top-quark decays, J / ψ and K * ( 892 ) 0 mesons in B -meson decays and ϕ mesons in χ c 0 and χ c 1 charmonium decays by reinterpreting the data and the analyses of the ATLAS, LHCb, Belle II and BESIII experimental collaborations, respectively. The polarization states of these four particles show contextuality with a significance larger than 5 σ . We also discuss the presence of quantum contextuality in spin states of bipartite systems formed by spin- 1 / 2 particles. We test Λ and Σ baryons reinterpreting two BESIII data analyses, and pairs of top quarks utilizing a recent analysis of the CMS Collaboration. Quantum contextuality is present with a significance exceeding 5 σ also in these cases. In addition, we study the feasibility of testing quantum contextuality by means of Z boson production in association with the Higgs boson, Z and W bosons pairs created in Higgs boson decays and with pairs of τ leptons. For the latter, we use Monte Carlo simulations that mimic the settings of SuperKEKB and of future lepton colliders. Experiments at high energies, though not designed for the purpose, perform surprisingly well in testing for quantum contextuality.
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for by 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 locality, Bell's theorem, and noncontextuality, due to Bell, Kochen and Specker (BKS). Noncontextuality is independent of nonlocality, and the contextuality manifests itself even in a single object. Here we report an experimental verification of quantum contextuality by a single spin-1 electron system at room temperature. Such a three-level system is indivisible and then we close the compatibility loophole which exists in the experiments performed on bipartite systems. Our results confirm the quantum contextuality to be the intrinsic property of single particles.
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.
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.