Single-shot Adaptive Measurement for Quantum-enhanced Metrology

TL;DR

This paper develops a formal framework for single-shot adaptive quantum metrology, using reinforcement learning to optimize feedback policies, achieving standard quantum limit precision with non-entangled particles.

Contribution

It introduces a decision-making formalism for AQEM and applies reinforcement learning to optimize feedback, a novel approach in quantum metrology.

Findings

Reinforcement learning effectively optimizes feedback policies.

Achieves SQL precision with non-entangled particles.

Provides a formal framework linking feedback to measurement precision.

Abstract

Quantum-enhanced metrology aims to estimate an unknown parameter such that the precision scales better than the shot-noise bound. Single-shot adaptive quantum-enhanced metrology (AQEM) is a promising approach that uses feedback to tweak the quantum process according to previous measurement outcomes. Techniques and formalism for the adaptive case are quite different from the usual non-adaptive quantum metrology approach due to the causal relationship between measurements and outcomes. We construct a formal framework for AQEM by modeling the procedure as a decision-making process, and we derive the imprecision and the Cram\'{e}r-Rao lower bound with explicit dependence on the feedback policy. We also explain the reinforcement learning approach for generating quantum control policies, which is adopted due to the optimal policy being non-trivial to devise. Applying a learning algorithm based on differential evolution enables us to attain imprecision for adaptive interferometric phase estimation, which turns out to be SQL when non-entangled particles are used in the scheme.