复合假设下Rabi信号的适应性检测
Adaptive detection of Rabi signals under composite hypotheses
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- Massachusetts Institute of Technology（麻省理工学院）
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中文总结 AI 辅助
该研究将固定预算下的重复量子传感建模为非对称复合假设检验，提出自适应策略利用后验信息选择投影轴，在Rabi信号检测中实现$n^{-1/2}$灵敏度并优于非自适应方法。
中文摘要 AI 辅助
受弱相干驱动搜索的启发，我们将固定预算下的重复量子传感表述为非对称复合假设检验。以Rabi传感为具体例子，我们在未知信号幅度和相位的共振情形下，对检测能力、灵敏度和第二类错误指数进行了基准测试。我们比较了非自适应的布居数读出和横向读出，以及一种近视贝叶斯策略，该策略通过最大化单步期望信息增益来选择每个投影轴。共同的决策统计量是对数贝叶斯因子，其策略特定的阈值在零假设下校准，以控制共同的第二类错误。弱信号展开表明，布居数读出与相位无关但对幅度呈二次依赖，给出$n^{-1/4}$灵敏度，而横向读出对幅度呈线性依赖，无需自适应即可达到$n^{-1/2}$灵敏度，但依赖于相位。在蒙特卡洛伪实验中，自适应策略利用关于未知方向的后验信息来指导后续读出；其灵敏度在模拟的大$n$范围内与$n^{-1/2}$一致，并且在最大的模拟射击次数下，优于固定的横向调度。其相位平均的有效第二类指数也超过了模拟范围内的非自适应参考。这些结果证明了在校准的假阳性控制下，利用干扰参数信息的有限预算价值。
英文摘要
Motivated by searches for weak coherent drives, we formulate repeated quantum sensing with a fixed shot budget as an asymmetric composite hypothesis test. Taking Rabi sensing as a concrete example, we benchmark detection power, sensitivity, and Type-II error exponents in the resonant case with unknown signal amplitude and phase. We compare non-adaptive population and transverse readouts with a myopic Bayesian policy that selects each projective axis by maximizing the expected information gain in one step. The common decision statistic is a log Bayes factor, with a policy specific threshold calibrated under the null to enforce a common Type-I error. A weak signal expansion shows that population readout is phase independent but quadratic in amplitude, giving $n^{-1/4}$ sensitivity, whereas transverse readout is linear in amplitude and permits $n^{-1/2}$ sensitivity without adaptation, but is phase-dependent. In Monte Carlo pseudoexperiments, the adaptive policy exploits posterior information about the unknown direction to guide subsequent readouts; its sensitivity is consistent with $n^{-1/2}$ over the simulated large $n$ range and, at the largest simulated shot counts, outperforms the fixed transverse schedules. Its phase-averaged effective Type-II exponent also exceeds the non-adaptive references over the simulated range. These results demonstrate the finite budget value of exploiting nuisance parameter information under calibrated false positive control.
