Saturating the one-axis twisting quantum Cram\'{e}r-Rao bound with a total spin readout

TL;DR

This paper demonstrates that a specific twist-untwist protocol with total spin measurement can asymptotically saturate the quantum Cramér-Rao bound in one-axis twisted spin interferometry, including finite-range interactions.

Contribution

The authors show that the twist-untwist protocol achieves the lowest quantum Cramér-Rao bound in spin interferometry, extending the analysis to finite-range interactions.

Findings

The metrological phase diagram is characterized by a single quantum Fisher information value $N(N+1)/2$.

The twist-untwist protocol's method of moments error saturates this Fisher information.

Finite-range interactions can also asymptotically reach the quantum Cramér-Rao bound with suitable protocols.

Abstract

We show that the lowest quantum Cram\'{e}r-Rao bound achievable in interferometry with a one-axis twisted spin coherent state is saturated by the asymptotic method of moments error of a protocol that uses one call to the one-axis twisting, one call to time-reversed one-axis twisting, and a final total spin measurement (i.e., a twist-untwist protocol). The result is derived by first showing that the metrological phase diagram for one-axis twisting is asymptotically characterized by a single quantum Fisher information value $N(N+1)/2$ for all times, then constructing a twist-untwist protocol having a method of moments error that saturates this value. The case of finite-range one-axis twisting is similarly analyzed, and a simple functional form for the metrological phase diagram is found in both the short-range and long-range interaction regimes. Numerical evidence suggests that the finite-range analogues of twist-untwist protocols can exhibit a method of moments error that asymptotically saturates the lowest quantum Cram\'{e}r-Rao bound achievable in interferometry with finite-range one-axis twisted spin coherent states for all interaction times.