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Proposed Direct Test of Quantum Contextuality

Karl Svozil

Published Feb 1, 2009• 1 citation
OpenAlex

Abstract

Quantum contextually can be directly tested by an Einstein-Podolsky-Rosen-type experiment of two spin one and higher particles in a singlet state. The two associated contexts are “interlinked” by a common observable.

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Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPR-type arrangement. On each side the Kochen-Specker observables {J 2 1,J 2 2,J 2 3} and { ¯ J 2 1, ¯ J 2 2,J 2 3} with [J 2 1, ¯ J 2 1] ̸= 0 are measured. The outcomes of measurements of J 2 3 (via J 2 1,J 2 2) and J 2 3 (via ¯ J 2 1, ¯ J 2 2) are compared. Although formally J 2 3 is associated with the same projection operator, quantum contextuality requires that the outcome depends on the complete disposition of the measurement apparatus, in particular whether J 2 1 or ¯ J 2 1 is measured alongside. Besides complementarity, contextuality [1, 2, 3, 4, 5] is another, more subtle nonclassical feature of quantum mechanics. That is, one and the same physical observable may appear different, depending on the context of measurement; i.e., depending on the particular way it was inferred. Stated differently, the outcome of a physical measurement may depend also on other physical measurements which are coperformed. In Bell’s own words [1, section 5], “The result of an
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.
We report a new two-photon polarization correlation experiment for realizing the Einstein-Podolsky-Rosen-Bohm (EPRB) state and for testing Bell-type inequalities. We use the pair of orthogonally-polarized light quanta generated in Type 2 parametric down conversion. Using 1 nm interference filters in front of our detectors, we observe from the output of a 0.5mm beta - BaB2O4 (BBO) crystal the EPRB correlations in coincidence counts, and measure an associated Bell inequality violation of 22 standard deviations. The quantum state of the photon pair is a polarization analog of the spin-1/2 singlet state.