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arXiv:2605.22917

Quantum Fisher Information under decoherence with explicit wavefunctions

Francesco Musso, Vittorio Vitale, Sara Murciano

quant-phcond-mat.stat-mechSubmitted May 21, 2026• Announced May 25, 2026• 0 citations
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Abstract

We present a method to estimate the quantum Fisher information (QFI) of many-body quantum states in the presence of decoherence, where its direct evaluation requires the full spectral resolution of the density matrix. We show that, for many-body wave functions known analytically in the occupation-number basis, systematic lower bounds to the QFI can be mapped onto expectation values over a classical probability distribution defined by the wave function amplitudes. This mapping enables efficient estimation via Markov-chain Monte Carlo sampling, with a computational cost that scales as a `slow' exponential ($e^{b L}$ with $b \lesssim 0.6$) and remains manageable for system sizes well beyond exact diagonalization. We specify this framework to Jastrow-Gutzwiller wave functions. We characterize their metrological content by identifying the observables that maximize the QFI and the corresponding scaling with $L$. Then, we analyze the QFI under three physically motivated noise channels: local dephasing, local amplitude damping, and global depolarizing. We compare polynomial and Krylov-based lower bounds across these channels, relating their behavior to the effective rank of the noisy density matrix and to the structure of the operator generating the parameter encoding. The framework extends naturally to other analytically known wave functions and to a broader class of information-theoretic quantities beyond the QFI.

Comments
11+10 pages, 5 figures, comments are welcome

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Quantum Fisher information (QFI) is a central concept in quantum sciences used to quantify the ultimate precision limit of parameter estimation, detect quantum phase transitions, witness genuine multipartite entanglement, or probe nonlocality. Despite this widespread range of applications, computing the QFI value of quantum many-body systems is, in general, a very demanding task. Here we combine ideas from functional theories and quantum information to develop a functional framework for the QFI of fermionic and bosonic ground states. By relying upon the constrained-search approach, we demonstrate that the QFI matrix terms can universally be determined by the one-body reduced density matrix (1-RDM), thus avoiding the use of exponentially large wave functions. Furthermore, we show that QFI functionals can be determined from the universal 1-RDM functional by calculating its derivatives with respect to the coupling strengths, thus becoming the generating functional of the QFI. We showcase our approach with the Bose-Hubbard model and present exact analytical and numerical QFI functionals. Our results provide the first connection between the one-body reduced density matrix functional theory and the quantum Fisher information. Published by the American Physical Society 2024
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Quantum Fisher information (QFI) is a fundamental quantifier in quantum metrology, determining the ultimate precision achievable in parameter-estimation protocols through the quantum Cramér-Rao bound. However, direct evaluation of the QFI generally requires detailed knowledge of the density matrix, making it increasingly demanding as the Hilbert-space dimension grows. In this work, we investigate the extent to which the QFI of multipartite quantum systems can be predicted from a limited set of experimentally accessible quantities using support vector regression (SVR). By comparing different physically motivated features, we identify a dominant feature set governing QFI and show that the predictive power of collective spin moments alone decreases as system size and consequently Hilbert-space dimension grows. We demonstrate that QFI is governed primarily by the interplay between collective covariance and low-order spectral moments of the density matrix. Our results identify the physically relevant information sectors governing the QFI and demonstrate that accurate estimation of metrological sensitivity can be achieved from a restricted set of experimentally accessible quantities without requiring full quantum-state tomography.
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We derive ultimate precision bounds for estimating parameters encoded in \emph{time-dependent} Hamiltonians in the presence of general Markovian noise, allowing for arbitrary adaptive protocols with fast controls and noiseless ancillas. Extending the minimization-over-purifications framework to time-varying continuous channels, we obtain a differential upper bound on the achievable quantum Fisher information (QFI) that can be evaluated at all times via semidefinite programming. For parameter-independent noise, we prove a universal long-time scaling law: if the coherent (noiseless) dynamics yields Qcoh(T)∼T2kQ_{\mathrm{coh}}(T)\sim T^{2k}Qcoh​(T)∼T2k, then under Markovian noise the QFI scales at most as Q(T)∼T2kQ(T)\sim T^{2k}Q(T)∼T2k in the DHNLS regime, whereas in the DHLS regime it is fundamentally limited to Q(T)∼T2k−1Q(T)\sim T^{2k-1}Q(T)∼T2k−1. We illustrate these behaviors on paradigmatic driven-qubit sensors, exhibiting T4T^{4}T4 and T3T^{3}T3 scalings under dephasing and spontaneous emission, respectively. Finally, we provide explicit continuous exact and approximate quantum error correction constructions -- supplemented by spin-squeezed probes -- that asymptotically saturate the bounds, establishing their tightness.
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