Saturating the one-axis twisting quantum Cramér-Rao bound with a total spin readout

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-23 DOI:10.1088/2399-6528/ad1dc8

T J Volkoff, Michael J Martin

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Abstract

We show that the lowest quantum Cramér-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 Cramér-Rao bound achievable in interferometry with finite-range one-axis twisted spin coherent states for all interaction times.

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用总自旋读出饱和单轴扭转量子克拉梅尔-拉奥约束

我们证明，在干涉测量中使用一轴扭转自旋相干态可达到的最低量子克拉梅尔-拉奥约束，在使用一次调用一轴扭转、一次调用时间反转一轴扭转和一次最终总自旋测量（即扭转-取消扭转协议）的协议中，其渐近矩法误差达到饱和。这一结果是通过首先证明单轴扭转的计量相图在所有时间内都渐近地由一个量子费雪信息值 N(N + 1)/2 来表征，然后构建一个扭转-解扭转协议，其矩量法误差达到该值的饱和。对有限范围单轴扭转的情况也进行了类似分析，并在短程和长程相互作用情况下为计量相图找到了一种简单的函数形式。数值证据表明，扭转-解扭转协议的有限范围类似方案可以表现出矩量法误差，在所有相互作用时间内，该误差渐近饱和有限范围单轴扭转自旋相干态干涉测量中可达到的最低量子克拉梅-拉奥约束。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.