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arXiv:2606.29795 · Physica Scripta

Nonlocal effects via Local Quantum Fisher Information: Characterizations and Interpretations

R. Muthuganesan

quant-phSubmitted Jun 29, 2026• Announced Jun 30, 2026• 0 citations
arXivHTMLPDF

Abstract

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

Journal reference
Phys. Scr. 101 (2026) 425103
DOI
10.1088/1402-4896/aeb3bf
Comments
10 pages, 3 Figures. Comments are welcome

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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
Abstract Measurement-induced nonlocality (MIN), a quantum correlation measure for bipartite systems, is an indicator of maximal global effects due to locally invariant von Neumann projective measurements. It is originally defined as the maximal square of the Hilbert–Schmidt norm of the difference between pre- and post-measurement states. In this article, we propose a new form of MIN based on affinity. This quantity satisfies all the criteria of a bona fide measure of quantum correlation measures. This quantity is evaluated for both arbitrary pure and 2 × n dimensional (qubit–qudit) mixed states. The operational meaning of the proposed quantity is interpreted in terms of the interferometric power of the quantum state. We apply these results on two-qubit mixed states, such as the Werner, isotropic and Bell diagonal states.
Abstract Quantum mechanics gives a new breakthrough to the field of parameter estimation. In the realm of quantum metrology, the precision of parameter estimation is limited by the quantum Fisher information. We introduce the measures of partial coherence based on (quantum) Fisher information by taking into account the post-selective non-unitary parametrization process. These partial coherence measures present a clear operational interpretation by directly linking the coherence to the parameter estimation accuracy. Furthermore, we explore the distinctions between our partial coherence measure and the quantum Fisher information within the context of unitary parametrization. We provide an analytical expression for the partial coherence measure of two-qubit states. We elucidate the operational significance of the partial coherence measures by establishing the connections between the partial coherence measures and quantum state discrimination.
We analyze the dynamics of the quantum Fisher information (QFI) in the case of a two-dimensional open quantum system obeying a time-local non-Markovian master equation in the canonical form, characterized by canonical decoherence rates and operators that depend on the parameter to be estimated. This last condition brings a framework in which the information about the parameter is structurally encoded not only in the open system, but also in the system-environment interaction or/and correlations, and in some environment properties. We derive analytical formulas for the decompositions of the QFI flow and of the purity dynamics in terms associated to the canonical decoherence rates. In contrast to the results presented in X.-M. Lu et al. [Phys. Rev. A 82, 042103 (2010)], we show that, in this extended framework, the QFI flow contains not only the subflows corresponding to the decoherence rates, but also supplementary terms which originate in the state dependence on the estimated parameter; moreover, the signs of the QFI subflows associated to the decoherence rates are not correlated to the signs of the rates. We show that a pertinent connection between the QFI flow and non-Markovianity can be realized using the canonical measures defined from the negative canonical decoherence rates. We employ this theoretical framework to explore the QFI flow and its subflows in two cases of quantum evolutions directed by master equations with decoherence rates or/and operators depending on the estimated parameter: (i) the Markovian nonunital time evolution of a qubit under the generalized amplitude damping channel; (ii) the non-Markovian time evolution of a two-dimensional electronic subsystem entangled with its vibrational environment in a molecule.
Measurements leading to the collapse of states and the non-local quantum correlations are the key to all applications of quantum mechanics as well as in the studies of quantum foundation. The former is crucial for quantum parameter estimation, which is greatly affected by the physical environment and the measurement scheme itself. Its quantification is necessary to find efficient measurement schemes and circumvent the non-desirable environmental effects. This has led to the intense investigation of quantum metrology, extending the Cramér–Rao bound to the quantum domain through quantum Fisher information. Among all quantum states, the separable ones have the least quantumness; being devoid of the fragile non-local correlations, the component states remain unaffected in local operations performed by any of the parties. Therefore, using these states for the remote design of quantum states with high quantum Fisher information can have diverse applications in quantum information processing; accurate parameter estimation being a prominent example, as the quantum information extraction solely depends on it. Here, we demonstrate that these separable states with the least quantumness can be made extremely useful in parameter estimation tasks, and further show even in the case of the shared channel inflicted with the amplitude damping noise and phase flip noise, there is a gain in Quantum Fisher information (QFI). We subsequently pointed out that the symmetric W states, incapable of perfectly teleporting an unknown quantum state, are highly effective for remotely designing quantum states with high quantum Fisher information.
Quantum Fisher information (QFI) quantifies the sensitivity of a quantum state to a parameter change and plays a key role in quantum metrology. Meanwhile, quantum coherence is a crucial resource for quantum information processing. However, despite extensive studies on various aspects of quantum metrology, the interplay between the dynamics of the QFI and quantum coherence remains unexplored. Here, we explore the factorization relationship between the QFI and quantum coherence, both theoretically and experimentally. We prepare pure states in qubit and qutrit systems and apply unitary evolution to investigate this relationship. Our results confirm the factorization law, offering strong evidence for this relationship. Furthermore, we establish a lower bound on the variance of the estimated parameter that does not require the final state information. This approach reveals a deep connection between the QFI and quantum coherence, providing insights into quantum parameter estimation. These findings have potential applications in quantum sensing and quantum metrology.
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.