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arXiv:2609.36571 · Science Advances

Factorization dynamics between quantum Fisher information and quantum coherence

Xinzhi Zhao, Xinglei Yu, Liangsheng Li, Wenting Zhou, Chengjie Zhang

quant-phSubmitted Sep 29, 2026• Announced Sep 30, 2026• 10 citations
arXivHTMLPDF

Abstract

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.

Journal reference
Science Advances 11, eadv8132 (2025)
DOI
10.1126/sciadv.adv8132
Comments
10+15 pages, 4+2 figures

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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.
This work explores the dynamics of quantum Fisher information (QFI) in open quantum systems coupled to squeezed reservoirs, providing a mathematical framework for analyzing parameter estimation precision under decoherence. We analyze QFI in two-qubit systems undergoing pure dephasing, considering the effects of squeezing parameter, phase difference, and coupling strength within an Ohmic spectral density model. The decoherence factor shows how reservoir engineering influences coherence loss. Numerical results demonstrate that optimal squeezing and local bath configurations enhance QFI preservation, while collective couplings accelerate decay. We also examine the interplay with von Neumann entropy, highlighting their inverse correlation, where increased mixedness reduces metrological sensitivity.
Abstract Quantum metrology is an important field in quantum information and plays a crucial role in quantum parameter estimation. Quantum Fisher information (QFI) is widely used to characterize the precision of quantum parameter estimation. However, a full understanding of the precision for different parameterization processes and the role of quantum evolutions in quantum parameter estimations, remains a crucial area of research. In this paper, we introduce a new concept, named as quantum Fisher information power (QFI power), to characterize the QFI-creating capability of quantum evolutions. At the same time, we take both unitary and non-unitary evolutions as examples and study QFI power. The results show that: (i) For unitary evolutions described by spin angular momentum operators, the dynamic of QFI power is dependent on the z component of the Bloch vector, and the rotating angle; (ii) For non-unitary evolutions under decoherence channels, QFI cannot be enhanced when the initial probe state belongs to zero QFI set, and the QFI power is negative when the initial probe state has maximal QFI; (iii) For the PT - and APT -symmetric non-unitary evolutions, the dynamics of QFI power exhibit oscillations in symmetry unbroken regime, while the phenomenon of stable value (SV) occurs in broken regimes with the SV = 1.
Quantum metrology is superior to classical metrology in parameter estimation. This is because quantum states have coherence that, however, does not exist in classical states. Previous works were limited to the study of the relationship between quantum Fisher information (QFI) and coherence of the initial probe state only for a specific single-qubit parameter estimation process (e.g., a process described by a single-qubit spin angular momentum operator Jz{J}_{z}Jz​). Here, we consider a more general case and study the relationship between QFI and coherence of the initial probe state for a single-qubit general parameter estimation process, which is described by a single-qubit spin angular momentum operator ${J}_{\stackrel{P\vec}{n}}$ with a general unit vector $\stackrel{P\vec}{n}$. We find that the QFI is proportional to the square of coherence of the initial probe state, when the single-qubit bases are eigenstates of the spin angular momentum operator ${J}_{\stackrel{P\vec}{n}}$ describing the parametrization process. We also design and conduct a linear optical experiment to support our theory. The experimental results are in good agreement with the theoretical ones. This work provides an important guideline for enhancing the precision of parameter estimation.
Recently various ways to quantify coherence of a quantum state have been proposed. In this paper, several reliable quantum coherence measures based on quantum Fisher information (QFI) are presented. For pure states, this coherence measure is equivalent to that based on skew information, while for mixed states, we first define two natural coherence measures via QFI and find that the two definitions are exactly identical. By virtual of the special structure of qubit, we show that the mutual unbiased bases' (MUBs) qubit coherence is constrained only by the length of the Bloch vector. Then we provide upper bounds of the coherence measure with respect to any given basis and lower bounds in the case of a set of MUBs for both pure states and mixed states of arbitrary dimension. Finally, we investigate the connection between our coherence measures and quantum metrology, thereby providing an operational meaning for these coherence measures.
Abstract The quantum Fisher information (QFI) plays a crucial role in quantum information theory and in many practical applications such as quantum metrology. However, computing the QFI is generally a computationally demanding task. In this work we analyze a lower bound on the QFI which we call the sub-quantum Fisher information (sub-QFI). The bound can be efficiently estimated on a quantum computer for an n -qubit state using 2 n qubits. The sub-QFI is based on the super-fidelity, an upper bound on Uhlmann’s fidelity. We analyze the sub-QFI in the context of unitary families, where we derive several crucial properties including its geometrical interpretation. In particular, we prove that the QFI and the sub-QFI are maximized for the same optimal state, which implies that the sub-QFI is faithful to the QFI in the sense that both quantities share the same global extrema. Based on this faithfulness, the sub-QFI acts as an efficiently computable surrogate for the QFI for quantum sensing and quantum metrology applications. Finally, we provide additional meaning to the sub-QFI as a measure of coherence, asymmetry, and purity loss.
Quantum coherence is one of the old but always important concepts in quantum mechanics, and now it has been regarded as a necessary resource for quantum information processing and quantum metrology. However, the question of how to quantify the quantum coherence has just been paid the attention recently (see, e.g., Baumgratz et al. PRL, 113. 140401 (2014)). In this paper we verify that the well-known quantum Fisher information (QFI) can be utilized to quantify the quantum coherence, as it satisfies the monotonicity under the typical incoherent operations and the convexity under the mixing of the quantum states. Differing from most of the pure axiomatic methods, quantifying quantum coherence by QFI could be experimentally testable, as the bound of the QFI is practically measurable. The validity of our proposal is specifically demonstrated with the typical phase-damping and depolarizing evolution processes of a generic single-qubit state, and also by comparing it with the other quantifying methods proposed previously.