The phase in quantum states is an essential information carrier for quantum telecommunications, signal processing, and computation. Quantum phase estimation is therefore a fundamental operation to extract and control useful information at the quantum level. Here, we analyze various approaches to quantum phase estimation, when a phase parameter characterizing a quantum process gets imprinted in a relative phase attached to a quantum state serving as a probe signal. The estimation approaches are based on standard concepts of signal processing (Fourier transform, maximum likelihood), yet operated in the quantum realm. We also exploit the Fisher information, both in its classical and its quantum forms, in order to assess the performance of each approach to quantum phase estimation. We demonstrate a possibility of enhanced estimation performance, inaccessible classically, which is obtained via optimized quantum entanglement. Beyond their significance to quantum phase estimation, the results illustrate how standard concepts of signal processing can contribute to the ongoing developments in quantum information and quantum technologies.

量子态的相位是量子电信，信号处理和计算的基本信息载体。因此，量子相位估计是在量子水平上提取和控制有用信息的基本操作。在这里，当表征表征量子过程的相位参数被压印在与作为探测信号的量子态相连的相对相位中时，我们分析量子相位估计的各种方法。估计方法基于信号处理的标准概念（傅立叶变换，最大似然），但仍在量子领域中运行。我们还利用经典形式和量子形式的Fisher信息，以评估每种量子相位估计方法的性能。我们证明了提高估算效果的可能性，这是通过优化的量子纠缠获得的经典方法所无法达到的。除了对量子相位估计的意义外，结果还说明了信号处理的标准概念如何有助于量子信息和量子技术的不断发展。