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Quantum Computing, Communication, and Simulation

Single-pair measurement of the Bell parameter

Ivo Pietro Degiovanni, S. Virzì, Enrico Rebufello, Francesco Atzori, Alessio Avella, Fabrizio Piacentini, Rudi Lussana, Iris Cusini, Francesca Madonini, Federica Villa, Marco Gramegna, Eliahu Cohen, Marco Genovese

Published Mar 19, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.3040665

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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.
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.
Abstract Bell inequalities represent one of the cornerstones of quantum foundations, and a fundamental tool for quantum technologies. Although a lot of effort was put in exploring and generalizing them, because of the wave function collapse it was deemed impossible to estimate the entire Bell parameter from one entangled pair, since this would involve measuring incompatible observables on the same quantum state. Conversely, here it is reported the first implementation of a new generation of Bell inequality tests, able to extract a Bell parameter value from each entangled pair and, at the same time, preserve the pair entanglement instead of destroying it. This is obtained by exploiting sequences of weak measurements, allowing incompatible observable measurements on a quantum state without collapsing its wave function. On the fundamental side, by removing the need to choose between different measurement bases our approach stretches the concept of counterfactual definiteness, since it allows measuring the entangled pair in all the bases needed for the Bell inequality test, intrinsically eliminating the issues connected with the otherwise not-chosen bases. On the practical side, after our Bell parameter measurement the entanglement within the pair remains (basically) unaltered, hence exploitable for other quantum-technology-related or foundational purposes.
Recently, an experiment was done in the realm of Quantum Information that won the recent 2022 Nobel prize in Physics. This experiment breaks Bell's inequality, supporting quantum theory over hidden variable theory—the research done is considered one of the pioneering experiments for quantum information science. This research paper documented the theory of the experiment done and experimentally tested for the violation of Bell's inequality, using materials similar to the experiments from the past, in an attempt to provide more support for quantum information. Through repetition of the experiment, it was simple to brainstorm more potential experimentation and design that will further develop entanglement. The mathematical formulation and terms are the same as defined in past works in detail in order to keep notation and inequalities constant throughout the analysis. Using the data points and error propagation, I have shown that Bell's inequality is violated to a great extent. This paper finally addresses potential experimentation regarding quantum entanglement and its applications to quantum sensors and computing technology.
This paper opens with a foundational exploration of basic concepts essential for understanding the Nobel Prize experiments. Next, some critical concepts directly related to the Nobel Prize will be introduced. We then delve into the recent Nobel Prize-awarded research. The heart of the discussion examines these groundbreaking experiments. The focus will be the process and the conclusion it made. Transitioning to practical applications, the focus shifts to how quantum entanglement is applied to quantum computation. The final part of this paper will be the conclusion and some predictions of the development of quantum physics.
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.
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)