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  • Open Access

Time Correlations from Steady-State Expectation Values

Wojciech Górecki1,*, Simone Felicetti2,3, Lorenzo Maccone1,4, and Roberto Di Candia5,2,4

  • *Present address: Freie Universität Berlin, Fachbereich Physik and Dahlem Center for Complex Quantum Systems, Arnimallee 14, 14195 Berlin.
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Phys. Rev. Lett. 137, 090401 – Published 25 August, 2026

DOI: https://doi.org/10.1103/24zv-dwcj

Abstract

Recovering properties of correlation functions is typically challenging. On the one hand, experimentally, it requires measurements with a temporal resolution finer than the system’s dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a system parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable, and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to the experimental characterization of ultrafast systems and to the theoretical analysis of many-body models whose dynamics are hard to compute.

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Outline

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Phys. Rev. Lett. 137, 090401– Published 25 August, 2026
  • Received 16 July 2025
  • Revised 14 November 2025
  • Accepted 5 August 2026
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