In quantum mechanics, the precision achieved in parameter estimation using a quantum state as a probe is determined by the measurement strategy employed. The quantum limit of precision is bounded by a value set by the state and its dynamics. Theoretical results have revealed that in interference measurements with two possible outcomes, this limit can be reached under ideal conditions of perfect visibility and zero losses. However, in practice, these conditions cannot be achieved, so precision never reaches the quantum limit. But how do experimental setups approach precision limits under realistic circumstances? In this Letter, we provide a model for precision limits in two-photon Hong-Ou-Mandel interferometry using coincidence statistics for nonperfect visibility and temporally unresolved measurements. We show that the scaling of precision with visibility depends on the effective area in time-frequency phase space occupied by the state used as a probe, and we find that an optimal scaling exists. We demonstrate our results experimentally for different states in a setup where the visibility can be controlled and reaches up to 99.5%. In the optimal scenario, a ratio of 0.97 is observed between the experimental precision and the quantum limit, establishing a new benchmark in the field.

中文翻译：

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接近非完美可见度红欧曼德尔干涉测量的最大精度

在量子力学中，使用量子态作为探针的参数估计所达到的精度取决于所采用的测量策略。精度的量子极限受到状态及其动力学设定的值的限制。理论结果表明，在具有两种可能结果的干扰测量中，在完美能见度和零损耗的理想条件下可以达到该极限。然而，在实践中，这些条件无法实现，因此精度永远不会达到量子极限。但实验装置如何在现实情况下接近精度极限呢？在这封信中，我们提供了一个双光子红欧曼德尔干涉测量中的精度限制模型，使用重合统计来实现非完美可见度和暂时无法解析的测量。我们表明，精度与可见性的缩放取决于用作探针的状态在时频相空间中占据的有效面积，并且我们发现存在最佳缩放。我们在可见度可以控制并达到 99.5% 的设置中通过实验展示了不同状态下的结果。在最佳场景下，实验精度与量子极限之比为0.97，树立了该领域的新基准。