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

LOCC-Maximized Quantum Fisher Information as a Necessary Condition for CHSH Violation

Volkan Erol

Published Oct 14, 2025• 0 citations
Publisher

Abstract

We investigate the relationship between CHSH inequality violation and quantum Fisher information (QFI) maximized over local operations and classical communication (LOCC) for two-qubit systems. Through systematic analysis of 1000 random states, we discover that no state with Bell parameter M(ρ) exceeding maximized QFI violates the CHSH inequality, suggesting QFImax serves as a necessary condition. States partition into three classes: (1) M(ρ) > QFImax with CHSH violation (23%), (2) M(ρ) > QFImax without violation (41%), and (3) M(ρ) < QFImax without violation (36%). We identify relative entropy of entanglement thresholds (0.14 and 0.26) separating regions of guaranteed violation, ambiguous behavior, and no violation. Furthermore, 98% of states exhibit QFI values that cross the separability bound under local rotations. These results provide efficient pre-screening criteria for device-independent quantum protocols and reveal deep connections between quantum metrology and Bell nonlocality.

DOI
10.20944/preprints201703.0223.v2

Related papers

Detecting Violation of Bell Inequalities using LOCC Maximized Quantum Fisher Information and Entanglement Measures

Volkan Erol

The violation of Bell's theorem is a very simple way to see that there is no underlying classical interpretation of quantum mechanics. The measurements made on the photons shows that light signal (information) could travel between them, hence completely eliminating any chance that the result was due to anything other than entanglement. Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. It was found that violation of Bell's inequalities could be trivially calculated and for sets of nonmaximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we visit violation of Bell's inequalities problem with a different approach. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with violation in Bell's inequalities and we make similar comparison of this violation with commonly studied entanglement measures, negativity and relative entropy of entanglement. We show that there are interesting orderings for system states.

•Mar 31, 2017•8 citations

Analysis of Entanglement Measures and LOCC Maximized Quantum Fisher Information of General Two Qubit Systems

Volkan Erol, Fatih Özaydin, Azmi Ali Altıntaṣ

Entanglement has been studied extensively for unveiling the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known measures for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. It was found that for sets of non-maximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we revisit the state ordering problem of general two qubit states. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with concurrence, REE and negativity and obtain new state orderings. We show that there are pairs of states having equal maximized QFI but different values for concurrence, REE and negativity and vice versa.

arXiv:1504.07767•Scientific Reports•Jun 24, 2014•56 citations

Empirical Modeling of Entanglement's Metrological Power via Maximized Quantum Fisher Information in Two-Qubit Systems

Volkan Erol

Abstract We provide a quantitative analysis of the connection between entanglement measures and Maximized Quantum Fisher Information (MQFI) using extensive numerical analysis of 20,000 randomly generated two-qubit states. Our systematic study reveals strong empirical relationships between the metrological capacity of quantum states and three entanglement measures: concurrence, negativity, and relative entropy of entanglement. Optimization over local unitary transformations produces substantially more predictable relationships than fixed-generator approaches, as confirmed by bootstrap resampling, systematic data binning, and multiple model comparisons. Exponential fits reach R 2 > 0.99 and polynomial models achieve R 2 = 0.999, providing thorough empirical support for saturation behavior in quantum metrological advantage. Even separable states possess robust metrological utility (MQFI/4 ≈ 0.19, p < 0.0001), achieving approximately 19% of maximal Bell-state sensing capacity—confirming the importance of quantum coherence and discord beyond entanglement. Entanglement–metrology relationships remain stable under realistic decoherence, particularly phase damping. Our findings empirically validate predictions from quantum resource theory, establish empirical bounds for quantum sensor optimization, and offer direct practical guidance for the design of quantum sensing protocols.

•May 18, 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

Maximal violation of Bell inequalities under local filtering

Ming Li, Huihui Qin, Jing Wang +2 more

We investigate the behavior of the maximal violations of the CHSH inequality and Vèrtesi's inequality under the local filtering operations. An analytical method has been presented for general two-qubit systems to compute the maximal violation of the CHSH inequality and the lower bound of the maximal violation of Vértesi's inequality over the local filtering operations. We show by examples that there exist quantum states whose non-locality can be revealed after local filtering operation by the Vértesi's inequality instead of the CHSH inequality.

arXiv:1704.08142•Scientific Reports•Apr 18, 2017•5 citations

Tight upper bound of the maximal quantum violation of Gisin’s elegant Bell inequality and its application in randomness certification

D. Hu, Menghan Li, Fen-Zhuo Guo +3 more

Abstract The violation of a Bell inequality implies the existence of nonlocality, making device-independent randomness certification possible. This paper derives a tight upper bound for the maximal quantum violation of Gisin’s elegant Bell inequality (EBI) for arbitrary two-qubit states, along with the constraints required to achieve this bound. This method provides the necessary and sufficient conditions for violating the EBI for several quantum states, including pure two-qubit states and the Werner states. The lower bound of certifiable global randomness is analyzed based on the tight upper bound of the EBI for pure two-qubit states, with a comparison to the Clauser-Horne-Shimony-Holt (CHSH) inequality. The relationship between the noise level and the lower bound of certifiable global randomness with respect to the Werner states is also explored, and the comparisons with both the CHSH inequality and the chained inequality are given. The results indicate that when the state approaches a maximally entangled state within specific quantified ranges, the EBI demonstrates advantages over both the CHSH inequality and the chained inequality, providing theoretical guidance for experimental device-independent quantum random number generation.

arXiv:2412.06345•EPJ Quantum Technology•Feb 10, 2025•8 citations
We investigate the relationship between CHSH inequality violation and quantum Fisher information (QFI) maximized over local operations and classical communication (LOCC) for two-qubit systems. Through systematic analysis of 1000 random states, we discover that no state with Bell parameter M(ρ) exceeding maximized QFI violates the CHSH inequality, suggesting QFImax serves as a necessary condition. States partition into three classes: (1) M(ρ) > QFImax with CHSH violation (23%), (2) M(ρ) > QFImax without violation (41%), and (3) M(ρ) < QFImax without violation (36%). We identify relative entropy of entanglement thresholds (0.14 and 0.26) separating regions of guaranteed violation, ambiguous behavior, and no violation. Furthermore, 98% of states exhibit QFI values that cross the separability bound under local rotations. These results provide efficient pre-screening criteria for device-independent quantum protocols and reveal deep connections between quantum metrology and Bell nonlocality.
The violation of Bell's theorem is a very simple way to see that there is no underlying classical interpretation of quantum mechanics. The measurements made on the photons shows that light signal (information) could travel between them, hence completely eliminating any chance that the result was due to anything other than entanglement. Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. It was found that violation of Bell's inequalities could be trivially calculated and for sets of nonmaximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we visit violation of Bell's inequalities problem with a different approach. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with violation in Bell's inequalities and we make similar comparison of this violation with commonly studied entanglement measures, negativity and relative entropy of entanglement. We show that there are interesting orderings for system states.
Entanglement has been studied extensively for unveiling the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known measures for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. It was found that for sets of non-maximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we revisit the state ordering problem of general two qubit states. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with concurrence, REE and negativity and obtain new state orderings. We show that there are pairs of states having equal maximized QFI but different values for concurrence, REE and negativity and vice versa.
Abstract We provide a quantitative analysis of the connection between entanglement measures and Maximized Quantum Fisher Information (MQFI) using extensive numerical analysis of 20,000 randomly generated two-qubit states. Our systematic study reveals strong empirical relationships between the metrological capacity of quantum states and three entanglement measures: concurrence, negativity, and relative entropy of entanglement. Optimization over local unitary transformations produces substantially more predictable relationships than fixed-generator approaches, as confirmed by bootstrap resampling, systematic data binning, and multiple model comparisons. Exponential fits reach R 2 > 0.99 and polynomial models achieve R 2 = 0.999, providing thorough empirical support for saturation behavior in quantum metrological advantage. Even separable states possess robust metrological utility (MQFI/4 ≈ 0.19, p < 0.0001), achieving approximately 19% of maximal Bell-state sensing capacity—confirming the importance of quantum coherence and discord beyond entanglement. Entanglement–metrology relationships remain stable under realistic decoherence, particularly phase damping. Our findings empirically validate predictions from quantum resource theory, establish empirical bounds for quantum sensor optimization, and offer direct practical guidance for the design of quantum sensing protocols.
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.
We investigate the behavior of the maximal violations of the CHSH inequality and Vèrtesi's inequality under the local filtering operations. An analytical method has been presented for general two-qubit systems to compute the maximal violation of the CHSH inequality and the lower bound of the maximal violation of Vértesi's inequality over the local filtering operations. We show by examples that there exist quantum states whose non-locality can be revealed after local filtering operation by the Vértesi's inequality instead of the CHSH inequality.
Abstract The violation of a Bell inequality implies the existence of nonlocality, making device-independent randomness certification possible. This paper derives a tight upper bound for the maximal quantum violation of Gisin’s elegant Bell inequality (EBI) for arbitrary two-qubit states, along with the constraints required to achieve this bound. This method provides the necessary and sufficient conditions for violating the EBI for several quantum states, including pure two-qubit states and the Werner states. The lower bound of certifiable global randomness is analyzed based on the tight upper bound of the EBI for pure two-qubit states, with a comparison to the Clauser-Horne-Shimony-Holt (CHSH) inequality. The relationship between the noise level and the lower bound of certifiable global randomness with respect to the Werner states is also explored, and the comparisons with both the CHSH inequality and the chained inequality are given. The results indicate that when the state approaches a maximally entangled state within specific quantified ranges, the EBI demonstrates advantages over both the CHSH inequality and the chained inequality, providing theoretical guidance for experimental device-independent quantum random number generation.