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Quantum Communications and Quantum Imaging

Measuring incompatible observables on entangled states through weak measurements: from single pair measurement of CHSH to testing relativistic independence

Marco Genovese, Enrico Rebufello

Published Sep 18, 2025• 0 citations
Publisher

Abstract

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)

DOI
10.1117/12.3062862

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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)
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.
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.
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.
Quantum correlations, like entanglement, represent the characteristic trait of quantum mechanics and pose essential issues and challenges to the interpretation of this pillar of modern physics. Although quantum correlations are largely acknowledged as a major resource to achieve quantum advantage in many tasks of quantum technologies, their full quantitative description and the axiomatic basis underlying them are still under investigation. Previous works have suggested that the origin of nonlocal correlations is grounded in principles capturing (from outside the quantum formalism) the essence of quantum uncertainty. In particular, the recently introduced principle of relativistic independence has given rise to a new bound intertwining local and nonlocal correlations. Here, we test such a bound by realizing together sequential and joint weak measurements on entangled photon pairs, allowing us to simultaneously quantify both local and nonlocal correlations by measuring incompatible observables on the same quantum system without collapsing its state, a task typically forbidden in the traditional (projective) quantum measurement framework. Our results demonstrate the existence of a fundamental limit on the extent of quantum correlations, shedding light on the profound role of uncertainty in both enabling and balancing them. Published by the American Physical Society 2024
Abstract Bell non-locality plays a fundamental role in quantum theory. Numerous tests of the Bell inequality have been reported as the ground-breaking discovery of the Bell theorem. Up to now, however, most discussions of the Bell scenario have focused on a single pair of entangled particles distributed to only two separated observers. Recently, it has been shown surprisingly that multiple observers can share the non-locality from an entangled pair using the method of weak measurement without post-selection [Phys. Rev. Lett. 114 , 250401 (2015)]. Here we report an observation of double CHSH-Bell inequality violations for a single pair of entangled photons with strength continuous-tunable optimal weak measurement in a photonic system. Our results shed new light on the interplay between non-locality and quantum measurements and our design of weak measurement protocol may also be significant for important applications such as unbounded randomness certification and quantum steering.