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This research establishes a fundamental quantum response kinetic uncertainty relation for continuously monitored open systems in steady states. By isolating a perturbation-induced intersubspace transition term absent in classical limits, the study clarifies genuine quantum contributions to measurement precision costs using symmetry-resolved decomposition. These theoretical bounds are critical for advancing our understanding of thermodynamic constraints in future quantum sensing and control protocols.
Response kinetic uncertainty relation for Markovian open quantum systems
arXiv:2501.04895v2 Announce Type: replace Abstract: Response uncertainty relations in stochastic thermodynamics extend precision bounds to the sensitivity of observables under external perturbations. Here we derive a quantum response kinetic uncertainty relation for continuously monitored Markovian open quantum systems in the steady state of the Lindblad master equation. The response precision of a measured trajectory observable is bounded by two contributions: the conventional quantum dynamical activity and a perturbation-induced intersubspace transition term. The latter is absent in the classical limit and captures a genuinely quantum part of the response cost. We identify simple conditions under which either contribution vanishes, and we further clarify the structure of the intersubspace term through a symmetry-resolved decomposition and exact sector-selection rules. The bound and its structure are illustrated in a driven two-level atom.
Abstract:Response uncertainty relations in stochastic thermodynamics extend precision bounds to the sensitivity of observables under external perturbations. Here we derive a quantum response kinetic uncertainty relation for continuously monitored Markovian open quantum systems in the steady state of the Lindblad master equation. The response precision of a measured trajectory observable is bounded by two contributions: the conventional quantum dynamical activity and a perturbation-induced intersubspace transition term. The latter is absent in the classical limit and captures a genuinely quantum part of the response cost. We identify simple conditions under which either contribution vanishes, and we further clarify the structure of the intersubspace term through a symmetry-resolved decomposition and exact sector-selection rules. The bound and its structure are illustrated in a driven two-level atom.
13 pages, 4 figures. This version substantially expands the original manuscript with operational upper bounds, symmetry-resolved intertransition analysis, non-unique steady-state discussion, etc
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2501.04895 [quant-ph]
(or arXiv:2501.04895v2 [quant-ph] for this version)
Phys. Rev. A 113, 062443 (2026)
https://doi.org/10.1103/ps1b-8l1x DOI(s) linking to related resources
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