Quantum Metrology in Open Systems: Dissipative Cram\'{e}r-Rao Bound

TL;DR

This paper develops a general framework for quantum parameter estimation in open systems, linking estimation precision to the system's dynamics and deriving a Cramér-Rao bound applicable to a broad class of open quantum processes.

Contribution

It introduces a new formulation of quantum metrology for open systems, deriving a Cramér-Rao bound based on dynamical semi-group maps, enabling improved estimation strategies.

Findings

Derived a Cramér-Rao bound for open quantum systems governed by dynamical semi-groups.

Illustrated the bound's utility through three practical examples.

Showed how system dynamics influence quantum estimation precision.

Abstract

Estimation of parameters is a pivotal task throughout science and technology. Quantum Cram\'{e}r-Rao bound provides a fundamental limit of precision allowed to achieve under quantum theory. For closed quantum systems, it has been shown how the estimation precision depends on the underlying dynamics. Here, we propose a general formulation for metrology scenarios in open quantum systems, aiming to relate the precision more directly to properties of the underlying dynamics. This feature may be employed to enhance an estimation precision, e.g., by quantum control techniques. Specifically, we derive a Cram\'{e}r-Rao bound for a fairly large class of open system dynamics, which is governed by a (time-dependent) dynamical semi-group map. We illustrate the utility of this scenario through three examples.