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

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

Volkan Erol

Published May 18, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.21203/rs.3.rs-9621779/v1

Related papers

Unveiling Entanglement's Metrological Power: Empirical Modeling of Optimal States in Quantum Metrics

Volkan Erol

Using extensive numerical analysis of 20,000 randomly generated two-qubit states, we provide a quantitative analysis of the connection between entanglement measures and Maximized Quantum Fisher Information (MQFI). Our systematic study shows strong empirical relationships between the metrological capacity of quantum states and three different entanglement measures: concurrence, negativity, and relative entropy of entanglement. We show that optimization over local unitary transformations produces substantially more predictable relationships than fixed-generator quantum Fisher information approaches using sophisticated statistical analysis, such as bootstrap resampling, systematic data binning, and multiple model comparisons. With exponential fits reaching $R^2 > 0.99$ and polynomial models reaching $R^2 = 0.999$, we offer thorough empirical support for saturation behavior in quantum metrological advantage. With immediate applications to realworld quantum sensing protocols, our findings directly empirically validate important predictions from quantum resource theory and set fundamental bounds for quantum sensor optimization and resource allocation. These intricate relationships are quantitatively described by the polynomial and exponential fit equations, which offer crucial real-world direction for the design of quantum sensors.

arXiv:2509.15954•Sep 19, 2025•0 citations

Mathematical Analysis of Entanglement Measures and Maximized Quantum Fisher Information

Volkan Erol

Entanglement measures such as concurrence, negativity and REE are well-known tools for quantifying non-classical correlations in quantum systems. However, these measures can lead to different state orderings for non-maximally entangled states. On the other hand, Quantum Fisher Information (QFI), while not an entanglement measure, provides a framework for analyzing a state's metrological potential. In this study, we numerically analyze the relationship between these entanglement measures and QFI for a large ensemble of random two-qubit states. We specifically focus on the maximized QFI (MQFI) obtained through local unitary rotations. Our findings demonstrate a strong correlation between entanglement and a state's metrological capacity, confirming that entanglement is a valuable resource. We show that while a state's QFI with a fixed generator can vary widely for a given entanglement value, local optimization to find the MQFI leads to a tighter, more predictable relationship. Our results also reinforce the principle that the metrological performance of all mixed states is fundamentally bounded by the theoretical limit of pure states. The polynomial fit equations for the upper and lower bounds of our data provide a quantitative description of these complex relationships.

•Sep 5, 2025•0 citations

Mathematical Analysis of Entanglement Measures and Maximized Quantum Fisher Information

Volkan Erol

Entanglement measures such as concurrence, negativity and REE are well-known tools for quantifying non-classical correlations in quantum systems. However, these measures can lead to different state orderings for non-maximally entangled states. On the other hand, Quantum Fisher Information (QFI), while not an entanglement measure, provides a framework for analyzing a state's metrological potential. In this study, we numerically analyze the relationship between these entanglement measures and QFI for a large ensemble of random two-qubit states. We specifically focus on the maximized QFI (MQFI) obtained through local unitary rotations. Our findings demonstrate a strong correlation between entanglement and a state's metrological capacity, confirming that entanglement is a valuable resource. We show that while a state's QFI with a fixed generator can vary widely for a given entanglement value, local optimization to find the MQFI leads to a tighter, more predictable relationship. Our results also reinforce the principle that the metrological performance of all mixed states is fundamentally bounded by the theoretical limit of pure states. The polynomial fit equations for the upper and lower bounds of our data provide a quantitative description of these complex relationships.

•Sep 18, 2025•0 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

Quantum Fisher Information and the Speed of Entanglement

Zain H. Saleem

We investigate the speed at which entanglement can be generated by an interaction parameter encoded in a two-qubit Hamiltonian, quantified by the derivative of concurrence with respect to the coupling parameter. For arbitrary pure two-qubit states evolving under a general nonlocal interaction, we derive a bound relating this entanglement speed to the quantum Fisher information (QFI). Specifically, we show that $|\partial_g C| \le \sqrt{F_Q^{(g)}} \sqrt{1-C^2}$, where $F_Q^{(g)}$ is the QFI associated with estimation of the parameter. This establishes $\sqrt{F_Q}\sqrt{1-C^2}$ as an upper bound on the speed of entanglement generation in parameter space. We further derive the saturation conditions and identify the states and dynamical regimes for which equality is attained. At saturation, concurrence evolves at the maximum rate permitted by the distinguishability of the underlying quantum state. These results reveal a direct connection between quantum metrology and entanglement generation, showing that the same information-theoretic quantity that governs parameter-estimation precision also limits the speed at which entanglement resources can be created.

quant-pharXiv:2606.15484•Physics Letters A•Jun 16, 2026•0 citations

Intrinsic relationships of Quantum Resource Theories and their roles in Quantum Metrology

Abdallah Slaoui

Quantum resource theories allow us to quantify a useful quantum phenomenon, to develop new protocols for its detection and determine the exact processes that maximize its use for practical tasks. These theories aim at transforming physical phenomena, such as entanglement and quantum coherence, into useful properties for the execution of concrete tasks related to quantum information. In this thesis, we focus on the resource theories of entanglement, discord-like quantum correlations, and quantum coherence, the most intriguing quantum phenomena exploited so far in quantum information theory. We begin by presenting in detail the theoretical tools of these quantum resources, focusing on the most remarkable techniques and computational problems. In this sense, we discuss several mathematical methods that solve some problems related to their quantifications, and some analytical results for bipartite quantum systems are given. We also examine the intrinsic connections between these quantum resources by extracting the links that unite the corresponding measures. In contrast, the revolution of quantum technology has led to a growing interest in quantum metrology, and quantum entanglement has been employed to overcome the classical limit in several quantum estimation protocols. In this work, we analyze the role of quantum correlations beyond entanglement in improving the accuracy of an unknown parameter. According to our results, correlations can be captured using quantum Fisher information, and quantum discord correlations can be exploited to ensure the accuracy of phase estimation protocols. This thesis includes also the contributions on the dynamics of these quantum resources in various models of open quantum systems. Among our objectives, is to study the effects of the environment on these quantum resources and to obtain techniques to protect them from the effects of intrinsic decoherence.

arXiv:2211.07975•Nov 15, 2022•0 citations
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.
Using extensive numerical analysis of 20,000 randomly generated two-qubit states, we provide a quantitative analysis of the connection between entanglement measures and Maximized Quantum Fisher Information (MQFI). Our systematic study shows strong empirical relationships between the metrological capacity of quantum states and three different entanglement measures: concurrence, negativity, and relative entropy of entanglement. We show that optimization over local unitary transformations produces substantially more predictable relationships than fixed-generator quantum Fisher information approaches using sophisticated statistical analysis, such as bootstrap resampling, systematic data binning, and multiple model comparisons. With exponential fits reaching R2>0.99R^2 > 0.99R2>0.99 and polynomial models reaching R2=0.999R^2 = 0.999R2=0.999, we offer thorough empirical support for saturation behavior in quantum metrological advantage. With immediate applications to realworld quantum sensing protocols, our findings directly empirically validate important predictions from quantum resource theory and set fundamental bounds for quantum sensor optimization and resource allocation. These intricate relationships are quantitatively described by the polynomial and exponential fit equations, which offer crucial real-world direction for the design of quantum sensors.
Entanglement measures such as concurrence, negativity and REE are well-known tools for quantifying non-classical correlations in quantum systems. However, these measures can lead to different state orderings for non-maximally entangled states. On the other hand, Quantum Fisher Information (QFI), while not an entanglement measure, provides a framework for analyzing a state's metrological potential. In this study, we numerically analyze the relationship between these entanglement measures and QFI for a large ensemble of random two-qubit states. We specifically focus on the maximized QFI (MQFI) obtained through local unitary rotations. Our findings demonstrate a strong correlation between entanglement and a state's metrological capacity, confirming that entanglement is a valuable resource. We show that while a state's QFI with a fixed generator can vary widely for a given entanglement value, local optimization to find the MQFI leads to a tighter, more predictable relationship. Our results also reinforce the principle that the metrological performance of all mixed states is fundamentally bounded by the theoretical limit of pure states. The polynomial fit equations for the upper and lower bounds of our data provide a quantitative description of these complex relationships.
Entanglement measures such as concurrence, negativity and REE are well-known tools for quantifying non-classical correlations in quantum systems. However, these measures can lead to different state orderings for non-maximally entangled states. On the other hand, Quantum Fisher Information (QFI), while not an entanglement measure, provides a framework for analyzing a state's metrological potential. In this study, we numerically analyze the relationship between these entanglement measures and QFI for a large ensemble of random two-qubit states. We specifically focus on the maximized QFI (MQFI) obtained through local unitary rotations. Our findings demonstrate a strong correlation between entanglement and a state's metrological capacity, confirming that entanglement is a valuable resource. We show that while a state's QFI with a fixed generator can vary widely for a given entanglement value, local optimization to find the MQFI leads to a tighter, more predictable relationship. Our results also reinforce the principle that the metrological performance of all mixed states is fundamentally bounded by the theoretical limit of pure states. The polynomial fit equations for the upper and lower bounds of our data provide a quantitative description of these complex relationships.
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.
We investigate the speed at which entanglement can be generated by an interaction parameter encoded in a two-qubit Hamiltonian, quantified by the derivative of concurrence with respect to the coupling parameter. For arbitrary pure two-qubit states evolving under a general nonlocal interaction, we derive a bound relating this entanglement speed to the quantum Fisher information (QFI). Specifically, we show that ∣∂gC∣≤FQ(g)1−C2|\partial_g C| \le \sqrt{F_Q^{(g)}} \sqrt{1-C^2}∣∂g​C∣≤FQ(g)​​1−C2​, where FQ(g)F_Q^{(g)}FQ(g)​ is the QFI associated with estimation of the parameter. This establishes FQ1−C2\sqrt{F_Q}\sqrt{1-C^2}FQ​​1−C2​ as an upper bound on the speed of entanglement generation in parameter space. We further derive the saturation conditions and identify the states and dynamical regimes for which equality is attained. At saturation, concurrence evolves at the maximum rate permitted by the distinguishability of the underlying quantum state. These results reveal a direct connection between quantum metrology and entanglement generation, showing that the same information-theoretic quantity that governs parameter-estimation precision also limits the speed at which entanglement resources can be created.
Quantum resource theories allow us to quantify a useful quantum phenomenon, to develop new protocols for its detection and determine the exact processes that maximize its use for practical tasks. These theories aim at transforming physical phenomena, such as entanglement and quantum coherence, into useful properties for the execution of concrete tasks related to quantum information. In this thesis, we focus on the resource theories of entanglement, discord-like quantum correlations, and quantum coherence, the most intriguing quantum phenomena exploited so far in quantum information theory. We begin by presenting in detail the theoretical tools of these quantum resources, focusing on the most remarkable techniques and computational problems. In this sense, we discuss several mathematical methods that solve some problems related to their quantifications, and some analytical results for bipartite quantum systems are given. We also examine the intrinsic connections between these quantum resources by extracting the links that unite the corresponding measures. In contrast, the revolution of quantum technology has led to a growing interest in quantum metrology, and quantum entanglement has been employed to overcome the classical limit in several quantum estimation protocols. In this work, we analyze the role of quantum correlations beyond entanglement in improving the accuracy of an unknown parameter. According to our results, correlations can be captured using quantum Fisher information, and quantum discord correlations can be exploited to ensure the accuracy of phase estimation protocols. This thesis includes also the contributions on the dynamics of these quantum resources in various models of open quantum systems. Among our objectives, is to study the effects of the environment on these quantum resources and to obtain techniques to protect them from the effects of intrinsic decoherence.