We study the problem of determining the photon number statistics of an unknown quantum state using conjugate optical homodyne detection. We quantify the information gain in a single-shot measurement and show that the photon number statistics can be recovered in repeated measurements on an ensemble of identical input states without scanning the phase of the input state or randomizing the phase of the local oscillator used in homodyne detection. We demonstrate how the expectation maximization algorithm and Bayesian inference can be utilized to facilitate the reconstruction and illustrate our approach by conducting experiments to study the photon number distributions of a weak coherent state and a thermal state source.

中文翻译：

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使用共轭光学零差检测来表征光子数统计。

我们研究使用共轭光学零差检测确定未知量子态的光子数统计量的问题。我们对单次测量中的信息增益进行量化，并表明可以在相同输入状态的集合中重复测量而恢复光子数统计，而无需扫描输入状态的相位或使零差中使用的本地振荡器的相位随机化检测。我们演示了如何利用期望最大化算法和贝叶斯推断来促进重构，并通过进行实验研究弱相干态和热态源的光子数分布来说明我们的方法。