We address the problem of distributed quantum metrology with a single squeezed-vacuum source by using the formalism of quantum mechanics in phase space. In particular, we demonstrate Heisenberg-limited sensitivity in the measurement of the average of two arbitrary phase shifts in the arms of a Mach–Zehnder interferometer. We obtain exact results for the measurement probability at the interferometer output for any value of the phases, which give us insight into the emergence of Heisenberg-limited sensitivity for periodical values of the phases.

中文翻译：

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马赫-曾德干涉仪平均相移的相空间海森堡有限估计

我们通过使用相空间中的量子力学形式来解决具有单个压缩真空源的分布式量子计量问题。特别是，我们在测量马赫-曾德干涉仪臂中两个任意相移的平均值时证明了海森堡有限的灵敏度。我们获得了干涉仪输出处任何相位值的测量概率的准确结果，这让我们深入了解了相位周期性值的海森堡限制灵敏度的出现。