Optimal quantum metrology under energy constraints

TL;DR

This paper develops a theoretical framework for quantum metrology under energy constraints, optimizing strategies to achieve the best possible precision while considering resource limitations, and reveals advantages of quantum superpositions of causal orders.

Contribution

It introduces a comprehensive method for optimizing energy-constrained quantum metrology and uncovers a new quantum advantage in energy efficiency using superpositions of causal orders.

Findings

Established the ultimate precision limit for energy-constrained phase estimation.

Identified quantum superpositions of causal orders as beneficial for energy-efficient quantum estimation.

Provided a general optimization approach for resource-limited quantum metrology.

Abstract

The traditional framework of quantum metrology commonly assumes unlimited access to resources, overlooking resource constraints in realistic scenarios. As such, the optimal strategies therein can be infeasible in practice. Here, we investigate quantum metrology where the total energy consumption of the probe state preparation, intermediate control operations, and the final measurement is subject to a constraint. We establish a comprehensive theoretical framework for characterizing energy-constrained multi-step quantum processes, based on which we develop a general optimization method for energy-constrained quantum metrology that determines both the optimal precision and the corresponding strategy. Using the method, we determine the ultimate precision limit of energy-constrained phase estimation and identify a novel advantage of quantum superpositions of causal orders in enhancing the energy efficiency of adaptive quantum estimation.