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arXiv · 2207.11462

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

T. J. Volkoff·Michael J. Martin
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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.

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T. J. Volkoff, Michael J. Martin. 2022-07-23. Saturating the one-axis twisting quantum Cram\'{e}r-Rao bound with a total spin readout. https://doi.org/10.1088/2399-6528%2Fad1dc8

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