Optical homodyne tomography consists in reconstructing the quantum state of an optical field from repeated measurements of its amplitude at different field phases (homodyne data). The experimental noise, which unavoidably affects the homodyne data, leads to a detection efficiency $\eta<1$ . The problem of reconstructing quantum states from noisy homodyne data sets prompted an intense scientific debate about the presence or absence of a lower homodyne efficiency bound ( $\eta> 0.5$ ) below which quantum features, like quantum interferences, cannot be retrieved. Here, by numerical experiments, we demonstrate that quantum interferences can be effectively reconstructed also for low homodyne detection efficiency. In particular, we address the challenging case of a Schrödinger cat state and test the minimax and adaptive Wigner function reconstruction technique by processing homodyne data distributed according to the chosen state but with an efficiency $\eta< 0.5$ . By numerically reproducing the Schrödinger’s cat interference pattern, we give evidence that quantum state reconstruction is actually possible in these conditions, and provide a guideline for handling optical tomography based on homodyne data collected by low efficiency detectors.

中文翻译：

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低零差检测效率的量子干扰重建

光学零差层析成像包括通过在不同场相位（谐调数据）上重复测量其振幅来重建光场的量子状态。实验噪声不可避免地影响零差数据，导致检测效率$ \ eta <1 $。从嘈杂的零差数据集重建量子状态的问题引发了关于是否存在较低零差效率界限（$ \ eta> 0.5 $）的激烈科学辩论，在该界限以下无法检索到量子特征，例如量子干扰。在这里，通过数值实验，我们证明了量子干扰也可以有效地重构，以降低零差检测效率。特别是，我们解决了Schrödinger猫状态的具有挑战性的情况，并通过处理根据所选状态分布的零差数据（效率为\\ eta <0.5 $）来测试minimax和自适应Wigner函数重构技术。通过数值再现薛定ding的猫干涉图，我们提供了在这些条件下实际上可以进行量子态重构的证据，并为基于低效率探测器收集的零差数据的光学层析成像提供了指导。