Fully-Optimized Quantum Metrology: Framework, Tools, and Applications

TL;DR

This paper presents a comprehensive framework for quantum metrology that determines the ultimate precision limits for various strategies using semidefinite programming, enabling optimal strategy identification and comparison.

Contribution

It introduces a systematic, semidefinite programming-based approach to find the maximal quantum Fisher information for diverse quantum sensing strategies, including indefinite causal order.

Findings

Exact optimal precision values for different strategies

Comparison of conventional and causally-indefinite strategies

Applications to noisy and non-Markovian quantum metrology

Abstract

This tutorial introduces a systematic approach for addressing the key question of quantum metrology: For a generic task of sensing an unknown parameter, what is the ultimate precision given a constrained set of admissible strategies. The approach outputs the maximal attainable precision (in terms of the maximum of quantum Fisher information) as a semidefinite program and optimal strategies as feasible solutions thereof. Remarkably, the approach can identify the optimal precision for different sets of strategies, including parallel, sequential, quantum SWITCH-enhanced, causally superposed, and generic indefinite-causal-order strategies. The tutorial consists of a pedagogic introduction to the background and mathematical tools of optimal quantum metrology, a detailed derivation of the main approach, and various concrete examples. As shown in the tutorial, applications of the approach include, but are not limited to, strict hierarchy of strategies in noisy quantum metrology, memory effect in non-Markovian metrology, and designing optimal strategies. Compared with traditional approaches, the approach here yields the exact value of the optimal precision, offering more accurate criteria for experiments and practical applications. It also allows for the comparison between conventional strategies and the recently discovered causally-indefinite strategies, serving as a powerful tool for exploring this new area of quantum metrology.