Improving the estimation of environment parameters via initial probe-environment correlations

TL;DR

This paper demonstrates that initial correlations between quantum probes and their environment can significantly enhance the precision of environment parameter estimation, especially when combined with control pulses, by increasing quantum Fisher information.

Contribution

It introduces a method to utilize initial probe-environment correlations to improve parameter estimation accuracy in quantum systems.

Findings

Initial correlations improve estimation precision.

Combining control pulses with initial correlations boosts Fisher information.

Order-of-magnitude increase in estimation accuracy achieved.

Abstract

Small, controllable quantum systems, known as quantum probes, have been proposed to estimate various parameters characterizing complex systems such as the environments of quantum systems. These probes, prepared in some initial state, are allowed to interact with their environment, and subsequent measurements reveal information about different quantities characterizing the environment such as the system-environment coupling strength, the cutoff frequency, and the temperature. These estimates have generally been made by considering only the way that the probe undergoes decoherence. However, we show that information about the environment is also imprinted on the probe via the probe and environment correlations that exist before the probe state preparation. This information can then be used to improve our estimates for any environment. We apply this general result to the particular case of a two-level system probe undergoing pure dephasing, due to a harmonic oscillator environment, to show that a drastic increase in the quantum Fisher information, and hence the precision of our estimates, can indeed be obtained. We also consider applying periodic control pulses to the probe to show that with a combination of the two - the effect of the control pulses as well as the initial correlations - the quantum Fisher information can be increased by orders of magnitude.