Unattainable & attainable bounds for quantum sensors

TL;DR

This paper clarifies the limitations of the quantum Cramer-Rao bound in quantum metrology, proposes optimal states for noiseless channel estimation under energy constraints, and suggests experimental methods for their generation to improve quantum sensing.

Contribution

It demonstrates that the quantum Cramer-Rao bound is not always attainable, identifies optimal states for energy-constrained noiseless channel estimation, and proposes experimental generation techniques using squeezing.

Findings

Quantum Cramer-Rao bound is not always attainable.

Optimal states for energy-constrained noiseless estimation are identified.

Proposed experimental generation of optimal states enhances quantum metrology.

Abstract

In quantum metrology, it is widely believed that the quantum Cramer-Rao bound is attainable bound while it is not true. In order to clarify this point, we explain why the quantum Cramer-Rao bound cannot be attained geometrically. In this manuscript, we investigate noiseless channel estimation under energy constraint for states, using a physically reasonable error function, and present the optimal state and the attainable bound. We propose the experimental generation of the optimal states for enhanced metrology using squeezing transformations. This makes the estimation of unitary channels physically implementable, while existing unitary estimation protocols do not work