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arXiv:2608.06359

Bell nonlocality from twisted statistics

Ivana Đorđ ević, Jovan Potrebić, Aleksandra Gočanin, Dragoljub Gočanin

quant-phSubmitted Aug 6, 2026• Announced Aug 7, 2026• 0 citations
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Abstract

We investigate Bell correlations for a free real quantum scalar field on the noncommutative Moyal plane. Although the free field dynamics and the one-particle sector remain unchanged, the deformation enters through twisted multiparticle statistics and its Fock-space dressing representation. A classical external source coupled locally to the twist-dressed quantum field prepares coherent superpositions of momentum-pair configurations propagating toward two spacelike-separated laboratories. The momentum-dependent twist phases are generally nonfactorizable and generate entanglement between the corresponding wave-packet modes. We show that suitable local mode measurements lead to a violation of the CHSH Bell inequality. The resulting correlations provide an operational probe of the noncommutative structure encoded in the multiparticle sector of the quantum field.

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12 pages, 1 figure

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Bell's theorem revealed the fundamental incompatibility between the predictions of quantum mechanics and local realism. Bell inequality violations have since demonstrated quantum nonlocality using photons and internal states of massive particles, but never using their motional states. Here we report the first Bell inequality violation in the motional states of massive particles. Using momentum-entangled pairs of metastable helium atoms manipulated by matter-wave interferometry, we measure a Clauser-Horne-Shimony-Holt (CHSH) Bell parameter of S=2.52±0.17S = 2.52 \pm 0.17S=2.52±0.17, violating the CHSH-Bell inequality (S≤2S \le 2S≤2). Our work completes a long-standing objective in quantum atom optics by extending Bell tests from internal quantum variables to the external degrees of freedom of massive particles, opening a new regime for exploring quantum nonlocality in matter waves and for investigating the interplay between quantum mechanics and gravity.
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