Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Dual-Use Bell Experiments for Quantum Polarimetry: Fisher-Information Certification from CHSH Data

Juan Sumaya-Martinez, José Javier Sánchez Mondragón

Published Jan 6, 2026• 0 citations
Publisher

Abstract

Bell-CHSH experiments with polarization-entangled photons are routinely performed to certify nonlocal correlations. We show that the \emph{same} dichotomic coincidence data can also serve as a quantitative metrological certificate for estimating a physical polarization parameter. Focusing on a local birefringent retardance $\phi$ applied to one photon, we (i) express the classical Fisher information (FI) for $\phi$ entirely in terms of CHSH correlators $E_{xy}(\phi)$, and (ii) derive an explicit lower bound on FI using only the observed CHSH data and the differential response $S'(\phi)$ of the Bell parameter. In the ideal two-qubit, unbiased-marginals regime, we further show a \emph{dual-use optimality}: the standard CHSH measurement settings simultaneously saturate the quantum Fisher information (QFI) for retardance estimation. We analyze robustness under depolarizing noise (visibility $v$) and outline a practical SPDC-based implementation requiring only standard polarization analysis. Our results provide an operational bridge between Bell nonlocality certification and precision metrology, while clarifying that large QFI and Bell nonlocality are not universally equivalent resources.

DOI
10.1364/opticaopen.30992950.v1

Related papers

Dual-Use Bell Experiments for Quantum Polarimetry: Fisher-Information Certification from CHSH Data

Juan Sumaya-Martinez, José Javier Sánchez Mondragón

Bell-CHSH experiments with polarization-entangled photons are routinely performed to certify nonlocal correlations. We show that the \emph{same} dichotomic coincidence data can also serve as a quantitative metrological certificate for estimating a physical polarization parameter. Focusing on a local birefringent retardance $\phi$ applied to one photon, we (i) express the classical Fisher information (FI) for $\phi$ entirely in terms of CHSH correlators $E_{xy}(\phi)$, and (ii) derive an explicit lower bound on FI using only the observed CHSH data and the differential response $S'(\phi)$ of the Bell parameter. In the ideal two-qubit, unbiased-marginals regime, we further show a \emph{dual-use optimality}: the standard CHSH measurement settings simultaneously saturate the quantum Fisher information (QFI) for retardance estimation. We analyze robustness under depolarizing noise (visibility $v$) and outline a practical SPDC-based implementation requiring only standard polarization analysis. Our results provide an operational bridge between Bell nonlocality certification and precision metrology, while clarifying that large QFI and Bell nonlocality are not universally equivalent resources.

•Jan 6, 2026•0 citations

Bell-certified retardance polarimetry from CHSH correlators

J. Sumaya-Martinez

Bell-CHSH measurements with polarization-entangled photons are commonly used as nonlocality witnesses. Here we show that the same coincidence data can also provide a quantitative metrological certificate for optical retardance sensing. For a local birefringent phase encoded on one photon, we derive the classical Fisher information directly from experimentally accessible CHSH correlators and obtain a lower bound expressed in terms of the measured correlations and the phase derivative of the CHSH parameter. In the unbiased-marginal two-qubit regime, the canonical CHSH analyzer settings are shown to be simultaneously Bell-optimal and Fisher-optimal, saturating the quantum Fisher information for retardance estimation in the ideal case. We further analyze reduced visibility, phase noise, analyzer misalignment, and finite coincidence counts, and construct conservative lower confidence bounds that can be evaluated without quantum-state tomography. The results also clarify that Bell violation and metrological usefulness are distinct resources: nonzero Fisher information can persist below the CHSH-violation threshold. The protocol therefore enables a standard Bell-test data set to provide both a nonlocality benchmark and a statistically controlled sensitivity certificate for quantum polarimetry.

quant-pharXiv:2609.23914•Sep 22, 2026•0 citations

Fisher-Information Certification from Bell Statistics: CHSH Bounds, Information Loss, and Finite-Data Guarantees

Juan Sumaya-Martínez, Omar Olmos-López, Jorge Mulia Rodríguez

Bell-test data are typically used to certify nonlocal correlations, while quantum metrology is concerned with the sensitivity of measurement statistics to unknown parameters. Here we connect these tasks at the level of experimentally accessible Bell statistics. Using standard moment-based Fisher-information inequalities, we derive lower bounds on the classical Fisher information directly from Bell scores and their parameter dependence, without requiring full state tomography. For CHSH measurements we establish a hierarchy between the information contained in the full outcome record, the set of individual correlators, and the compressed Bell parameter, thereby quantifying the metrological cost of data compression. In polarization-phase sensing, this hierarchy reveals a Bell-metrology tradeoff: the point of maximal CHSH violation need not maximize, and can even suppress, the Fisher information carried by the Bell score itself. We further derive finite-sample lower-confidence bounds from coincidence counts and analyze the effects of biased marginals, accidental coincidences, visibility loss, and multipair emission. The framework provides a practical route for extracting metrological guarantees from Bell-type experiments using only standard correlation measurements.

quant-pharXiv:2610.16702•Oct 13, 2026•0 citations

Bell-certified retardance polarimetry from CHSH correlators

Juan Sumaya-Martinez

Bell--CHSH measurements with polarization-entangled photons are usually reported only as nonlocality witnesses. Here we show that, for retardance sensing, the same coincidence data can also provide a quantitative metrological certificate. For a local birefringent phase $\phi$ encoded on one photon, we derive the classical Fisher information directly from experimentally accessible CHSH correlators $E_{xy}(\phi)$ and obtain an explicit lower bound in terms of the measured correlators and the phase slope $S'(\phi)$ of the Bell parameter. In the unbiased-marginal two-qubit regime, this leads to a dual-use result: the canonical CHSH analyzer settings are simultaneously Bell-optimal and Fisher-optimal, saturating the quantum Fisher information for retardance estimation. We further show that the certificate remains informative under visibility loss, finite counts, and moderate departure from the Bell-violation threshold, so useful retardance sensitivity can persist even when nonlocality certification is weak or absent. Relative to tomography-based entangled-photon polarimetry, the method converts a standard Bell-calibration run into a sensitivity statement with rigorous lower confidence bounds using only coincidence correlators. The scheme is implementable with standard SPDC sources, wave plates, and polarizing beam splitters.

•May 7, 2026•0 citations

Nonlocal effects via Local Quantum Fisher Information: Characterizations and Interpretations

R. Muthuganesan

We introduce a quantum Fisher information based measurement-induced nonlocality (QFI-MIN), which quantifies the maximal statistical distinguishability induced by locally invariant unitary dynamics. The proposed measure inherits desirable properties including positivity, local unitary invariance, monotonicity under local operations, and immunity to the local ancilla problem. Analytical expressions are obtained for pure states, arbitrary two-qubit states, and two-qubit X states, revealing a direct connection with entanglement for pure systems. We further establish clear operational interpretations of QFI-MIN in quantum parameter estimation, local channel discrimination, and correlation-assisted communication. Its behavior under amplitude damping, depolarizing, and generalized amplitude damping channels demonstrates robustness against environmental noise. The proposed framework provides a physically consistent and operationally meaningful quantifier of quantum correlations, linking nonlocality, quantum metrology, and quantum information processing

quant-pharXiv:2606.29795•Physica Scripta•Jun 30, 2026•0 citations

Quantum Nonlocality and Device-Independent Randomness Robust to Relaxations of Bell Assumptions

Ravishankar Ramanathan, Yuan Liu

The question of certifying quantum nonlocality under a relaxation of the assumptions in the Bell theorem has gained traction, with potential for device-independent applications under weak seeds and cross-talk. Recently, it was shown that quantum nonlocality can be certified even under a simultaneous arbitrary (but not full) relaxation of the assumptions of Measurement Independence (MI) and Parameter Independence (PI), using states of local dimension $d = poly((1-ε)^{-1})$ for an $ε\in [0,1)$-relaxation. Here, we derive three results strengthening the state-of-art. Firstly, we show that states of constant local dimension $d$ are already sufficient to certify quantum nonlocality under arbitrary MI and PI relaxation, albeit in a non-robust manner. Secondly, and as a theoretical paradigm to derive the above, we introduce the notion of \textit{measurement-dependent parameter-dependent locality} as the set of input-output behaviors under simultaneous relaxations of measurement and parameter independence. We provide a rigorous characterisation of the vertices of the polytope of joint input-output behaviors that obey a $μ$-relaxation of MI and $ε$-relaxation of PI. We highlight a relation between nonlocality certification under PI relaxation and that under detection inefficiencies by pointing out alternative extremal correlations to the Eberhard correlations that also allow to achieve detection efficiency of $η= 2/3$ in the two-input scenario. Finally, we study the implication of the relaxed assumptions for device-independent randomness certification. We analytically derive the quantum guessing probability for one player's outcomes in the CHSH Bell test, as a function of the noise in the test as well as of a leakage of an average amount of $I(X:B) < 1$ bits of input information per measurement round.

quant-pharXiv:2512.18513•Dec 23, 2025•0 citations
Bell-CHSH experiments with polarization-entangled photons are routinely performed to certify nonlocal correlations. We show that the \emph{same} dichotomic coincidence data can also serve as a quantitative metrological certificate for estimating a physical polarization parameter. Focusing on a local birefringent retardance ϕ\phiϕ applied to one photon, we (i) express the classical Fisher information (FI) for ϕ\phiϕ entirely in terms of CHSH correlators Exy(ϕ)E_{xy}(\phi)Exy​(ϕ), and (ii) derive an explicit lower bound on FI using only the observed CHSH data and the differential response S′(ϕ)S'(\phi)S′(ϕ) of the Bell parameter. In the ideal two-qubit, unbiased-marginals regime, we further show a \emph{dual-use optimality}: the standard CHSH measurement settings simultaneously saturate the quantum Fisher information (QFI) for retardance estimation. We analyze robustness under depolarizing noise (visibility vvv) and outline a practical SPDC-based implementation requiring only standard polarization analysis. Our results provide an operational bridge between Bell nonlocality certification and precision metrology, while clarifying that large QFI and Bell nonlocality are not universally equivalent resources.
Bell-CHSH experiments with polarization-entangled photons are routinely performed to certify nonlocal correlations. We show that the \emph{same} dichotomic coincidence data can also serve as a quantitative metrological certificate for estimating a physical polarization parameter. Focusing on a local birefringent retardance ϕ\phiϕ applied to one photon, we (i) express the classical Fisher information (FI) for ϕ\phiϕ entirely in terms of CHSH correlators Exy(ϕ)E_{xy}(\phi)Exy​(ϕ), and (ii) derive an explicit lower bound on FI using only the observed CHSH data and the differential response S′(ϕ)S'(\phi)S′(ϕ) of the Bell parameter. In the ideal two-qubit, unbiased-marginals regime, we further show a \emph{dual-use optimality}: the standard CHSH measurement settings simultaneously saturate the quantum Fisher information (QFI) for retardance estimation. We analyze robustness under depolarizing noise (visibility vvv) and outline a practical SPDC-based implementation requiring only standard polarization analysis. Our results provide an operational bridge between Bell nonlocality certification and precision metrology, while clarifying that large QFI and Bell nonlocality are not universally equivalent resources.
Bell-CHSH measurements with polarization-entangled photons are commonly used as nonlocality witnesses. Here we show that the same coincidence data can also provide a quantitative metrological certificate for optical retardance sensing. For a local birefringent phase encoded on one photon, we derive the classical Fisher information directly from experimentally accessible CHSH correlators and obtain a lower bound expressed in terms of the measured correlations and the phase derivative of the CHSH parameter. In the unbiased-marginal two-qubit regime, the canonical CHSH analyzer settings are shown to be simultaneously Bell-optimal and Fisher-optimal, saturating the quantum Fisher information for retardance estimation in the ideal case. We further analyze reduced visibility, phase noise, analyzer misalignment, and finite coincidence counts, and construct conservative lower confidence bounds that can be evaluated without quantum-state tomography. The results also clarify that Bell violation and metrological usefulness are distinct resources: nonzero Fisher information can persist below the CHSH-violation threshold. The protocol therefore enables a standard Bell-test data set to provide both a nonlocality benchmark and a statistically controlled sensitivity certificate for quantum polarimetry.
Bell-test data are typically used to certify nonlocal correlations, while quantum metrology is concerned with the sensitivity of measurement statistics to unknown parameters. Here we connect these tasks at the level of experimentally accessible Bell statistics. Using standard moment-based Fisher-information inequalities, we derive lower bounds on the classical Fisher information directly from Bell scores and their parameter dependence, without requiring full state tomography. For CHSH measurements we establish a hierarchy between the information contained in the full outcome record, the set of individual correlators, and the compressed Bell parameter, thereby quantifying the metrological cost of data compression. In polarization-phase sensing, this hierarchy reveals a Bell-metrology tradeoff: the point of maximal CHSH violation need not maximize, and can even suppress, the Fisher information carried by the Bell score itself. We further derive finite-sample lower-confidence bounds from coincidence counts and analyze the effects of biased marginals, accidental coincidences, visibility loss, and multipair emission. The framework provides a practical route for extracting metrological guarantees from Bell-type experiments using only standard correlation measurements.
Bell--CHSH measurements with polarization-entangled photons are usually reported only as nonlocality witnesses. Here we show that, for retardance sensing, the same coincidence data can also provide a quantitative metrological certificate. For a local birefringent phase ϕ\phiϕ encoded on one photon, we derive the classical Fisher information directly from experimentally accessible CHSH correlators Exy(ϕ)E_{xy}(\phi)Exy​(ϕ) and obtain an explicit lower bound in terms of the measured correlators and the phase slope S′(ϕ)S'(\phi)S′(ϕ) of the Bell parameter. In the unbiased-marginal two-qubit regime, this leads to a dual-use result: the canonical CHSH analyzer settings are simultaneously Bell-optimal and Fisher-optimal, saturating the quantum Fisher information for retardance estimation. We further show that the certificate remains informative under visibility loss, finite counts, and moderate departure from the Bell-violation threshold, so useful retardance sensitivity can persist even when nonlocality certification is weak or absent. Relative to tomography-based entangled-photon polarimetry, the method converts a standard Bell-calibration run into a sensitivity statement with rigorous lower confidence bounds using only coincidence correlators. The scheme is implementable with standard SPDC sources, wave plates, and polarizing beam splitters.
We introduce a quantum Fisher information based measurement-induced nonlocality (QFI-MIN), which quantifies the maximal statistical distinguishability induced by locally invariant unitary dynamics. The proposed measure inherits desirable properties including positivity, local unitary invariance, monotonicity under local operations, and immunity to the local ancilla problem. Analytical expressions are obtained for pure states, arbitrary two-qubit states, and two-qubit X states, revealing a direct connection with entanglement for pure systems. We further establish clear operational interpretations of QFI-MIN in quantum parameter estimation, local channel discrimination, and correlation-assisted communication. Its behavior under amplitude damping, depolarizing, and generalized amplitude damping channels demonstrates robustness against environmental noise. The proposed framework provides a physically consistent and operationally meaningful quantifier of quantum correlations, linking nonlocality, quantum metrology, and quantum information processing
The question of certifying quantum nonlocality under a relaxation of the assumptions in the Bell theorem has gained traction, with potential for device-independent applications under weak seeds and cross-talk. Recently, it was shown that quantum nonlocality can be certified even under a simultaneous arbitrary (but not full) relaxation of the assumptions of Measurement Independence (MI) and Parameter Independence (PI), using states of local dimension d=poly((1−ε)−1)d = poly((1-ε)^{-1})d=poly((1−ε)−1) for an ε∈[0,1)ε\in [0,1)ε∈[0,1)-relaxation. Here, we derive three results strengthening the state-of-art. Firstly, we show that states of constant local dimension ddd are already sufficient to certify quantum nonlocality under arbitrary MI and PI relaxation, albeit in a non-robust manner. Secondly, and as a theoretical paradigm to derive the above, we introduce the notion of \textit{measurement-dependent parameter-dependent locality} as the set of input-output behaviors under simultaneous relaxations of measurement and parameter independence. We provide a rigorous characterisation of the vertices of the polytope of joint input-output behaviors that obey a μμμ-relaxation of MI and εεε-relaxation of PI. We highlight a relation between nonlocality certification under PI relaxation and that under detection inefficiencies by pointing out alternative extremal correlations to the Eberhard correlations that also allow to achieve detection efficiency of η=2/3η= 2/3η=2/3 in the two-input scenario. Finally, we study the implication of the relaxed assumptions for device-independent randomness certification. We analytically derive the quantum guessing probability for one player's outcomes in the CHSH Bell test, as a function of the noise in the test as well as of a leakage of an average amount of I(X:B)<1I(X:B) < 1I(X:B)<1 bits of input information per measurement round.