Quantum metrology for non-Markovian processes

TL;DR

This paper develops a comprehensive framework for quantum metrology in non-Markovian processes, providing formulas and algorithms to optimize quantum Fisher information and demonstrating improved sensing performance over Markovian cases.

Contribution

It introduces a general theoretical framework and computational methods for non-Markovian quantum metrology, extending beyond the well-studied Markovian case.

Findings

Non-Markovian processes can enhance quantum sensing performance.

An algorithm for evaluating quantum Fisher information via semidefinite programming.

Potential for efficient sensing using simple variational circuits.

Abstract

Quantum metrology is a rapidly developing branch of quantum technologies. While various theories have been established on quantum metrology for Markovian processes, i.e., quantum channel estimation, quantum metrology for non-Markovian processes is much less explored. In this Letter, we establish a general framework of non-Markovian quantum metrology. For any parametrized non-Markovian process on a finite-dimensional system, we derive a formula for the maximal amount of quantum Fisher information that can be extracted from it by an optimally controlled probe state. In addition, we design an algorithm that evaluates this quantum Fisher information via semidefinite programming. We apply our framework to noisy frequency estimation, where we find that the optimal performance of quantum metrology is better in the non-Markovian scenario than in the Markovian scenario and explore the possibility of efficient sensing via simple variational circuits.