Versatile probe state preparation via generalized measurements for quantum sensing and thermometry

TL;DR

This paper presents a flexible quantum probe state preparation method using generalized measurements to improve parameter estimation in quantum sensing, applicable to thermometry and decay rate characterization.

Contribution

It introduces a measurement-based protocol to tailor probe states for enhanced quantum parameter estimation, linking quantum Fisher information with thermodynamic properties.

Findings

Probe states can be optimized for specific estimation tasks.

The protocol modulates quantum Fisher information significantly.

Analytical relationship established between Fisher information, susceptibilities, and Hamiltonian variance.

Abstract

We investigate a probe state preparation protocol based on two non-selective generalized quantum measurements to enhance parameter estimation in single-qubit systems. By fine-tuning the measurement strengths, we demonstrate the ability to design a broad class of probe states, initially prepared in a thermal state, which can be optimized for specific estimation tasks. We apply this framework to characterize the decay rate and the temperature of a generalized amplitude damping channel. Our results show that the preparation protocol significantly modulates the quantum Fisher information for both parameters. Furthermore, we derive a general analytical relationship between the quantum Fisher information, thermodynamic susceptibilities, and Hamiltonian variance, valid even in the transient regime. This connection highlights the role of energy fluctuations and kinetic response in determining metrological precision. Finally, we briefly discuss a quantum circuit for experimental implementation using nuclear magnetic resonance techniques.