Quantum Metrology for Non-Markovian Processes

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.

Automated summary

This letter establishes a general framework for non-Markovian quantum metrology, deriving a formula for extracting maximal quantum Fisher information from parametrized non-Markovian processes on finite-dimensional systems. An algorithm is designed to evaluate this information using semidefinite programming. The framework is applied to noisy frequency estimation, showing better performance in non-Markovian scenarios compared to Markovian ones.