The use of an interferometer to perform an ultra-precise parameter estimation under noisy conditions is a challenging task. Here we discuss nearly optimal measurement schemes for a well known, sensitive input state, squeezed vacuum and coherent light. We find that a single mode intensity measurement, while the simplest and able to beat the shot-noise limit, is outperformed by other measurement schemes in the low-power regime. However, at high powers, intensity measurement is only outperformed by a small factor. Specifically, we confirm, that an optimal measurement choice under lossless conditions is the parity measurement. In addition, we also discuss the performance of several other common measurement schemes when considering photon loss, detector efficiency, phase drift, and thermal photon noise. We conclude that, with noise considerations, homodyne remains near optimal in both the low and high power regimes. Surprisingly, some of the remaining investigated measurement schemes, including the previous optimal parity measurement, do not remain even near optimal when noise is introduced.

中文翻译：

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具有相干和压缩真空的嘈杂Mach-Zehnder干涉仪中的最佳测量方案

使用干涉仪在嘈杂的条件下执行超精确的参数估计是一项艰巨的任务。在这里，我们讨论了一种众所周知的敏感输入状态，压缩真空和相干光的近乎最佳的测量方案。我们发现，单模强度测量虽然最简单且能够克服散粒噪声限制，但在低功率方案中却比其他测量方案要好。但是，在高功率下，强度测量仅表现出很小的优势。具体来说，我们确认，无损条件下的最佳测量选择是奇偶校验测量。此外，在考虑光子损耗，检测器效率，相位漂移和热光子噪声时，我们还将讨论其他几种常见测量方案的性能。我们得出的结论是，考虑到噪声，在低功率和高功率两种情况下，零差都保持最佳状态。令人惊讶的是，当引入噪声时，包括先前的最佳奇偶校验测量在内的其余一些研究的测量方案甚至都无法保持最佳状态。