Optimal Strategies of Quantum Metrology with a Strict Hierarchy

TL;DR

This paper develops a systematic framework to determine the ultimate precision limits in quantum metrology across various strategy families, revealing a strict hierarchy of achievable precisions.

Contribution

It introduces an efficient algorithm to identify optimal strategies within different quantum metrology families and establishes a hierarchy of their precision limits.

Findings

Existence of a strict hierarchy of precision limits among strategy families

Development of an efficient algorithm for optimal strategy identification

Framework applicable to parallel, sequential, and indefinite-causal-order strategies

Abstract

One of the main quests in quantum metrology is to attain the ultimate precision limit with given resources, where the resources are not only of the number of queries, but more importantly of the allowed strategies. With the same number of queries, the restrictions on the strategies constrain the achievable precision. In this work, we establish a systematic framework to identify the ultimate precision limit of different families of strategies, including the parallel, the sequential, and the indefinite-causal-order strategies, and provide an efficient algorithm that determines an optimal strategy within the family of strategies under consideration. With our framework, we show there exists a strict hierarchy of the precision limits for different families of strategies.