Effect of system–reservoir correlations on temperature estimation*

Abstract

In many previous temperature estimation schemes, the temperature of a sample is directly read out from the final steady state of a quantum probe, which is coupled to the sample. However, in these studies, information of correlations between system (the probe) and reservoir (the sample) is usually eliminated, leading the steady state of the probe is a canonical equilibrium state with respect solely to system’s Hamiltonian. To explore the influence of system–reservoir correlations on the estimation precision, we investigate the equilibration dynamics of a spin interacting with a finite temperature bosonic reservoir. By incorporating an intermediate harmonic oscillator or a collective coordinate into the spin, the system–reservoir correlations can be correspondingly encoded in a Gibbs state of an effective Hamilton, which is size consistent with the original bare spin. Extracting information of temperature from this corrected steady state, we find the effect of the system-reservoir correlations on the estimation precision is highly sensitive to the details of the spectral density function of the measured reservoir.

Non-Markovian temperature sensing

“…Under such treatment, one can see the frequency shift Ω → Ω shall lead to a smaller value of gg (∞)/ ee (∞) [see Figs. 4(a) and 5(a)] compared with that of the canonical Gibbs state case, which implies the breakdown of canonical statistics [62][63][64]. Moreover, if Ω > Ω * , the frequency renormalization results in a larger QFI in comparison with that of the canonical statistics [see Fig.…”

Environmental parameter estimation with the two-level atom probes

“…At present, many schemes have been proposed to improve the estimation precision of the temperature with quantum estimation theory, such as a ring-structure system interacting with the bath, [40] twolevel atoms transported through an optical cavity, [41] a uniformly accelerated two-level atom coupled to a massless scalar field in the Minkowski vacuum, [42] and the probe system embedded into the structured reservoir. [43][44][45][46][47] However, the model that the two-level system (qubit) is directly immersed in a ther-mal reservoir has not been utilized for the temperature estimation. In addition, several researchers have reported that the squeezed state or reservoir has the potential to protect the nonclassical effects of the quantum system [48] and improve the accuracy of phase estimation.…”