多路径干涉测量中可预测性与量子相干性之间的权衡及其操作解释
Trade-off between predictability and quantum coherence for multi-path interferometry and its operational interpretation
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中文总结 AI 辅助
研究多路径设置下可预测性与量子相干性的互补关系，引入基于基的可预测性，推导二者权衡关系，该关系赋予相干性度量操作解释，为源独立量子随机数生成器的猜测概率提供最坏情况界限。
中文摘要 AI 辅助
互补原理是量子力学的基石。在本工作中，我们研究了在多路径设置下，分别代表波粒二象性中粒子样和波样行为的可预测性与量子相干性之间的互补关系。我们引入了一种基于基的可预测性，由所选基中退相态与最大混合态之间的Bures距离定义。可预测性仅取决于观测到的基统计量，并以Bhattacharyya重叠的形式给出封闭形式。我们推导了可预测性与基于Kirkwood-Dirac准概率非经典性定义的相干性度量之间的权衡关系。对于纯态，权衡关系是精确相等的。值得注意的是，这种波粒二象性关系赋予相干性度量一种操作解释，即作为测量随机性的经典不可约部分，在源独立量子随机数生成器中对猜测概率产生严格的最坏情况界限。
英文摘要
The complementarity principle is a cornerstone of quantum mechanics. In this work, we investigate a complementarity relation between the predictability and quantum coherence, respectively, representing the particle-like and wave-like behaviour in wave--particle duality, in a multi-path setup. We introduce a basis-dependent predictability defined by the Bures distance between the state dephased in the chosen basis and the maximally mixed state. The predictability depends only on the observed basis statistics and admits a closed form in terms of the Bhattacharyya overlap. We derive a trade-off relation between the predictability and a coherence measure defined based on the nonclassicality of the Kirkwood--Dirac quasiprobability. For pure states, the trade-off relation is an exact equality. Remarkably, this wave--particle duality relation endows the coherence measure with an operational interpretation as the classically irreducible part of measurement randomness, yielding a tight worst-case bound on the guessing probability in source-independent QRNG.
