Georgiev, Danko; Cohen, Eliahu Analysis of single-particle nonlocality through the prism of weak measurements. (English) Zbl 1441.81023 Int. J. Quantum Inf. 18, No. 1, Article ID 1941024, 31 p. (2020). Summary: Although regarded today as an important resource in quantum information, nonlocality has yielded over the years many conceptual conundrums. Among the latter are nonlocal aspects of single particles which have been of major interest. In this paper, the nonlocality of single quanta is studied in a square nested Mach-Zehnder interferometer with spatially separated detectors using a delayed choice modification of quantum measurement outcomes that depend on the complex-valued weak values. We show that if spacelike separated Bob and Alice are allowed to freely control their quantum devices, the geometry of the setup constrains the local hidden variable models. In particular, hidden signaling and a list of contextual instructions are required to split a quantum state characterized by a positive Wigner function into two quantum states with nonpositive Wigner functions. This implies that local hidden variable models could rely neither on only two hidden variables for position and momentum, nor on simultaneous factorizability of both the hidden probability densities and weights of splitting to reproduce the correct quantum distributions. While our analysis does not fully exclude the existence of nonfactorizable local hidden variable models, it demonstrates that the recently proposed weak values of quantum histories necessitate contextual splitting of prior commitments to measurement outcomes, due to functional dependence on the total Feynman sum that yields the complex-valued quantum probability amplitude for the studied quantum transition. This analysis also highlights the quantum nature of weak measurements. Cited in 1 Document MSC: 81P40 Quantum coherence, entanglement, quantum correlations 81P13 Contextuality in quantum theory 81P15 Quantum measurement theory, state operations, state preparations 46G10 Vector-valued measures and integration 81P45 Quantum information, communication, networks (quantum-theoretic aspects) 81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics 81P65 Quantum gates 81P05 General and philosophical questions in quantum theory Keywords:nonlocality; contextuality; weak measurements; weak values × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Einstein, A., Causality, determinism, probability, in Quantum Theory at the Cross-Roads: Reconsidering the 1927 Solvay Conference, eds. Bacciagaluppi, G. and Valentini, A. (Cambridge University Press, Cambridge, 2009), pp. 440-442. [2] Guerreiro, T., Sanguinetti, B., Zbinden, H., Gisin, N. and Suarez, A., Phys. Lett. A376 (2012) 2174. 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