Quantum state discrimination is a central problem in quantum measurement theory, with applications spanning from quantum communication to computation. Typical measurement paradigms for state discrimination involve a minimum probability of error or unambiguous discrimination with a minimum probability of inconclusive results. Alternatively, an optimal inconclusive measurement, a non-projective measurement, achieves minimal error for a given inconclusive probability. This more general measurement encompasses the standard measurement paradigms for state discrimination and provides a much more powerful tool for quantum information and communication. Here, we experimentally demonstrate the optimal inconclusive measurement for the discrimination of binary coherent states using linear optics and single-photon detection. Our demonstration uses coherent displacement operations based on interference, single-photon detection, and fast feedback to prepare the optimal feedback policy for the optimal non-projective quantum measurement with high fidelity. This generalized measurement allows us to transition among standard measurement paradigms in an optimal way from minimum error to unambiguous measurements for binary coherent states. As a particular case, we use this general measurement to implement the optimal minimum error measurement for phase-coherent states, which is the optimal modulation for communications under the average power constraint. Moreover, we propose a hybrid measurement that leverages the binary optimal inconclusive measurement in conjunction with sequential, unambiguous state elimination to realize higher dimensional inconclusive measurements of coherent states.

量子态判别是量子测量理论中的一个核心问题，其应用范围从量子通信到计算。状态歧视的典型测量范式涉及最小概率的错误或明确的歧视，具有最小概率的不确定结果。或者，对于给定的不确定概率，最优的不确定测量，即非投影测量，实现了最小的误差。这种更通用的测量包含状态辨别的标准测量范式，并为量子信息和通信提供了更强大的工具。在这里，我们通过实验证明了使用线性光学和单光子检测来区分二元相干态的最佳不确定测量。我们的演示使用基于干涉、单光子检测和快速反馈的相干位移操作来为具有高保真度的最佳非投影量子测量准备最佳反馈策略。这种广义测量允许我们以最佳方式在标准测量范式之间转换，从最小误差到二进制相干状态的明确测量。作为一个特殊情况，我们使用这种通用测量来实现相位相干状态的最佳最小误差测量，这是平均功率约束下的通信的最佳调制。此外，我们提出了一种混合测量，它利用二元最优非结论性测量与顺序测量相结合，