Applications of quantum technology often require fidelities to quantify performance. These provide a fundamental yardstick for the comparison of two quantum states. While this is straightforward in the case of pure states, it is much more subtle for the more general case of mixed quantum states often found in practice. A large number of different proposals exist. In this review, we summarize the required properties of a quantum fidelity measure, and compare them, to determine which properties each of the different measures has. We show that there are large classes of measures that satisfy all the required properties of a fidelity measure, just as there are many norms of Hilbert space operators, and many measures of entropy. We compare these fidelities, with detailed proofs of their properties. We also summarize briefly the applications of these measures in teleportation, quantum memories and quantum computers, quantum communications, and quantum phase-space simulations.

中文翻译：

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混合态的量子保真度测量

量子技术的应用通常需要保真度来量化性能。这些为比较两个量子态提供了一个基本的尺度。虽然这在纯态的情况下很简单，但对于实践中经常发现的混合量子态的更一般情况，它要微妙得多。存在大量不同的提议。在这篇综述中，我们总结了量子保真度度量所需的属性，并比较它们，以确定每个不同度量具有哪些属性。我们表明，存在大量满足保真度度量的所有必需属性的度量，就像希尔伯特空间算子的许多范数和熵的许多度量一样。我们将这些保真度与其属性的详细证明进行了比较。