无损马赫-曾德尔干涉仪中的量子计量,使用纠缠光子输入进行一系列非自适应和自适应测量

IF 4.2 Q2 QUANTUM SCIENCE & TECHNOLOGY
Shreyas Sadugol, Lev Kaplan
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引用次数: 0

摘要

利用多光子纠缠输入态,利用光子计数检测估计了无噪声马赫-曾德尔干涉仪的相位不确定性。我们假设一个平坦的先验不确定性,并使用贝叶斯推理构造一个后验不确定性。通过最小化后验方差以获得最优输入状态,我们首先设计了一种估计和测量策略,该策略可以为单个测量产生最低的相位不确定性。在某些情况下,确定N00N和高斯态是最优的。然后,我们推广到一系列重复测量,使用非自适应和完全自适应测量。在这些情况下,N00N和高斯输入状态也接近最优,并给出了最优解析公式。使用这些公式作为输入,得到了一个通用的缩放公式,该公式显示了将相位不确定性降低到目标水平平均需要多少次射击。最后,将这些理论结果与使用频率推理的蒙特卡罗模拟进行了比较。在两种推理方法中,局部非自适应方法被证明是降低相位不确定性最有效的实用方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Quantum metrology in a lossless Mach–Zehnder interferometer using entangled photon inputs for a sequence of non-adaptive and adaptive measurements
Using multi-photon entangled input states, we estimate the phase uncertainty in a noiseless Mach–Zehnder interferometer using photon-counting detection. We assume a flat prior uncertainty and use Bayesian inference to construct a posterior uncertainty. By minimizing the posterior variance to get the optimal input states, we first devise an estimation and measurement strategy that yields the lowest phase uncertainty for a single measurement. N00N and Gaussian states are determined to be optimal in certain regimes. We then generalize to a sequence of repeated measurements, using non-adaptive and fully adaptive measurements. N00N and Gaussian input states are close to optimal in these cases as well, and optimal analytical formulae are developed. Using these formulae as inputs, a general scaling formula is obtained, which shows how many shots it would take on average to reduce phase uncertainty to a target level. Finally, these theoretical results are compared with a Monte Carlo simulation using frequentist inference. In both methods of inference, the local non-adaptive method is shown to be the most effective practical method to reduce phase uncertainty.
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CiteScore
9.90
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