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Temperature and non-Markovian parameter estimation in quantum Brownian motion

João C. P. Porto1,*, Carlos H. S. Vieira2,†, Irismar G. da Paz1, Pedro R. Dieguez3, and Lucas S. Marinho1,‡

  • 1Departamento de Física, Universidade Federal do Piauí, Campus Ministro Petrônio Portela, CEP 64049-550, Teresina, Piauí, Brazil
  • 2Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Avenida dos Estados 5001, 09210-580 Santo André, São Paulo, Brazil
  • 3International Centre for Theory of Quantum Technologies, University of Gdańsk, Jana Bażyńskiego 1A, 80-309 Gdańsk, Poland

  • *Contact author: carlosciaufpi@gmail.com
  • †Contact author: vieira.carlos@ufabc.edu.br
  • ‡Contact author: lucas.marinho@ufpi.edu.br

Phys. Rev. A 112, 042424 – Published 15 October, 2025

DOI: https://doi.org/10.1103/c87r-22mn

Abstract

We investigate a quantum metrological protocol operating in a non-Markovian environment by employing the quantum Brownian motion model, in which the system is linearly coupled to a reservoir of harmonic oscillators. Specifically, we use a position-momentum (PM) correlated Gaussian state as a probe to examine how memory effects influence the evolution of the system's covariance matrix in the weak-coupling regime under both high- and low-temperature conditions. To confirm the presence of non-Markovian behavior, we apply two well-established non-Markovianity quantifiers. Furthermore, we estimate both the channel's sample temperature and its non-Markovianity witness parameter. Our results demonstrate that non-Markovianity and PM correlations can jointly be valuable resources to enhance metrological performance.

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