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arXiv:2409.02510 · Physical Review A

Consequences of the single-pair measurement of the Bell parameter

Marco Genovese, Fabrizio Piacentini

Published Feb 4, 2025• 6 citations
arXivHTMLPDF

Abstract

Bell inequalities represent a milestone for contemporary physics, both for quantum foundation investigations and technological applications (e.g., quantum communication and entanglement certification). Although loophole-free tests have been recently performed, a strong debate is still ongoing on the actual meaning of Bell inequality tests, for example, on the possible additional hypotheses and eventual loopholes to be included in Bell's theorem, as well as on the implications for certain interpretations of quantum mechanics. A recent work [S. Virzì , ] challenges some of the statements appeared in this debate, achieving an experimental estimation of the entire Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) parameter from a single entangled pair owing to a weak-interaction-based measurement approach. Here, we analyze the implications of this result for quantum mechanics foundations investigation, illustrating how it can tackle some of the aforementioned interpretations of Bell inequality tests and, more in general, of quantum mechanics itself.

DOI
10.1103/physreva.111.022204

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Comment on “Consequences of the single-pair measurement of the Bell parameter”

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In a recent article [], Genovese and Piacentini analyzed recent experiments measuring what they call “the entire Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) parameter.” They claimed those experiments may have implications for interpreting loophole-free tests of the Bell-CHSH inequality. We explain that the Bell-CHSH inequality is not based on the entire Bell parameter, so these experiments are unrelated to their empirical tests and cannot close any eventual loopholes that might still persist. We point out that the physical meaning of these new experiments measuring the entire Bell parameter could be interpreted differently.

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Comment on “Consequences of the single-pair measurement of the Bell parameter”

Marian Kupczyński

Genovese and Piacentini [] claim that, in a recent experiment [S. Virzì , ], the Bell parameter was measured on a single pair of photons, thus challenging several conclusions and discussions on the meaning of Bell inequalities as well as certain quantum mechanical interpretations. We explain that the parameter measured in the experiment of Virzì is not the Bell parameter S , which has been discussed and estimated in many loophole-free tests. Therefore, this experiment neither challenges our understanding of Bell tests nor allows having doubts about Bohr complementarity and contextuality.

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Measuring incompatible observables on entangled states through weak measurements: from single pair measurement of CHSH to testing relativistic independence. F.Piacentini, A.Avella, E.Rebufello, S. Virzì, I.P.Degiovanni, M.Gramegna, M.Genovese We present the first single-pair Bell inequality test [1] able to obtain a Bell parameter value for every entangled pair detected. This is made possible by exploiting sequential weak measurements, allowing to perform non-commuting measurements in sequence on the same state, on each entangled particle. Such a feature removes the need to choose between different measurement bases [2]. We also demonstrate how, after the Bell parameter measurement, the pair under test still presents a noteworthy amount of entanglement, providing evidence of the absence of the wave function collapse and allowing us to exploit this quantum resource for further protocols. Finally, as a further use of sequential weak measurement, we present a test [3] of the relativistic independence. [1] S.Virzì, et al. Quant.Sci. Tech. 9 045027 (2024) [2] M.Genovese & F.Piacentini, arXiv:2409.02510 [3] F.Atzori rt al., PRX quantum 5, 040351 (2024)

Quantum Communications and Quantum Imaging•Sep 18, 2025•0 citations
Bell inequalities represent a milestone for contemporary physics, both for quantum foundation investigations and technological applications (e.g., quantum communication and entanglement certification). Although loophole-free tests have been recently performed, a strong debate is still ongoing on the actual meaning of Bell inequality tests, for example, on the possible additional hypotheses and eventual loopholes to be included in Bell's theorem, as well as on the implications for certain interpretations of quantum mechanics. A recent work [S. Virzì , ] challenges some of the statements appeared in this debate, achieving an experimental estimation of the entire Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) parameter from a single entangled pair owing to a weak-interaction-based measurement approach. Here, we analyze the implications of this result for quantum mechanics foundations investigation, illustrating how it can tackle some of the aforementioned interpretations of Bell inequality tests and, more in general, of quantum mechanics itself.
In a recent article [], Genovese and Piacentini analyzed recent experiments measuring what they call “the entire Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) parameter.” They claimed those experiments may have implications for interpreting loophole-free tests of the Bell-CHSH inequality. We explain that the Bell-CHSH inequality is not based on the entire Bell parameter, so these experiments are unrelated to their empirical tests and cannot close any eventual loopholes that might still persist. We point out that the physical meaning of these new experiments measuring the entire Bell parameter could be interpreted differently.
Genovese and Piacentini [] claim that, in a recent experiment [S. Virzì , ], the Bell parameter was measured on a single pair of photons, thus challenging several conclusions and discussions on the meaning of Bell inequalities as well as certain quantum mechanical interpretations. We explain that the parameter measured in the experiment of Virzì is not the Bell parameter S , which has been discussed and estimated in many loophole-free tests. Therefore, this experiment neither challenges our understanding of Bell tests nor allows having doubts about Bohr complementarity and contextuality.
Abstract This chapter presents a detailed discussion of Bell inequalities and their experimental tests. Starting from the Aharonov-Bohm version of the Einstein-Podolsky-Rosen (EPR) paradox, we review EPR’s criteria for realism and completeness and Bell’s locality condition, before deriving the Clauser-Horne-Shimony-Holt (CHSH) inequality. This is followed by an exposition on Bell’s original inequality and other Bell inequalities by Wigner, as well as Clauser and Horne. We then discuss the milestones in the experimental violation of Bell inequalities, from the experiment of Freedman and Clauser in the 1970s, to the efforts of Aspect et al. in the 1980s, the experiments by the teams of Zeilinger and Gisin in the 1990s, and culminating the loophole-free tests in 2015. Finally we turn to a brief discussion of the interpretations of quantum mechanics, focusing on contrasting the realist views held by, e.g., Einstein and Bell, and the informational views with proponents such as Brukner and Zeilinger
Since their formulation, Bell inequalities have been one of the pillars of quantum foundations and quantum information, also representing a tool of the utmost relevance for quantum technologies, e.g. for quantum communication A long path, awarded by the 2022 Nobel prize, has gone along since their introduction, finally reaching conclusive Bell inequality violations in 2015. However, none of the experiments run so far was able to extract information on the entire Bell inequality from every entangled pair measured, because of the wavefunction collapse. Here we illustrate an actual paradigm shift in this perspective, since we experimentally demonstrate the possibility of extracting information on the full Bell parameter (specifically the CHSH one) from each entangled pair measured and, at the same time, still conserving most of the pair entanglement after the measurement.
Many future directions of scientific endeavors depend on quantum theory and the precise interpretation and significance of the entanglement of quantum-particles. This interpretation depends in turn on the physical meaning of so called Bell-tests that are mostly performed using entangled photons and randomly switched polarizers to measure their polarization at distant locations. This paper presents a detailed critique of the well known theory of Bell tests given by Clauser-Horne-Shimony-Holt (CHSH). It is demonstrated that several important steps of the CHSH derivations contain serious inaccuracies of the underlying physics and probability theory and even a calculus error. As a consequence, the Bell-CHSH theory cannot be used to demonstrate extreme and opposite interpretations of entanglement such as super-luminal influences or alternatively super-determinism that cast aspersions on Einstein’s concepts of locality and separability.
Measuring incompatible observables on entangled states through weak measurements: from single pair measurement of CHSH to testing relativistic independence. F.Piacentini, A.Avella, E.Rebufello, S. Virzì, I.P.Degiovanni, M.Gramegna, M.Genovese We present the first single-pair Bell inequality test [1] able to obtain a Bell parameter value for every entangled pair detected. This is made possible by exploiting sequential weak measurements, allowing to perform non-commuting measurements in sequence on the same state, on each entangled particle. Such a feature removes the need to choose between different measurement bases [2]. We also demonstrate how, after the Bell parameter measurement, the pair under test still presents a noteworthy amount of entanglement, providing evidence of the absence of the wave function collapse and allowing us to exploit this quantum resource for further protocols. Finally, as a further use of sequential weak measurement, we present a test [3] of the relativistic independence. [1] S.Virzì, et al. Quant.Sci. Tech. 9 045027 (2024) [2] M.Genovese & F.Piacentini, arXiv:2409.02510 [3] F.Atzori rt al., PRX quantum 5, 040351 (2024)