Finite-Size Effects in Quantum Metrology at Strong Coupling: Microscopic vs Phenomenological Approaches

Abstract:Equilibrium quantum metrology is often formulated under assumptions of weak system-bath coupling and thermodynamic limit scaling, which may not be valid for realistic finite-size (FS) quantum devices. Here, we establish how strong coupling (SC) and FS effects jointly modify achievable precision bounds for equilibrium quantum probes. Considering a transverse-field anisotropic XY spin chain coupled to a thermal environment, first utilize we derive a full polaron transform to derive the effective Hamiltonian at equilibrium. Then, using the bare Hamiltonian and the obtained effective Hamiltonian and taking into account the role of FS effects in the calculation of partition function, we derive an analytic expressions for the quantum Fisher information (QFI) for a general parameter for the equilibrium state in weak coupling (WC) and SC regimes, respectively. In contrast to this microscopic approach, we also utilize the Hill's phenomenological nanothermodynamics to calculate an effective QFI expression at SC. Our results, presented for specific cases of magnetometry and thermometry, reveal that considering FS and SC effects lead to substantial and systematic deviations in QFI, even for moderate system sizes, and that commonly used thermodynamic-limit approximations can significantly misestimate precision. This work also highlights the inadequacy of phenomenological approaches in describing the metrological capability and thermodynamic behavior of systems at SC. Our work establishes a consistent framework for evaluating metrological performance of realistic, finite quantum devices operating beyond the weak-coupling paradigm.

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2507.19994 [quant-ph]

(or arXiv:2507.19994v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2507.19994 Focus to learn more arXiv-issued DOI via DataCite

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