Quantifying the quantumness of ensembles is a vital and practical task in quantum information theory. In this paper, we quantify the quantumness of quantum ensembles based on a quantifier of the coherence of ensembles via generalized α-z-relative Renyi entropy. It is shown that this measure satisfies the intuitive and desirable properties which are required by a measure of quantumness, such as positivity, unitary invariance, monotonicity under any commutativity preserving operations and so on. The relationship between our measure and some existing measures for quantumness of quantum ensembles is discussed. Detailed examples are presented to some important ensembles to illustrate the quantumness given by our measure.

中文翻译：

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通过广义 α-z-relative rényi 熵量化集合的量子性

量化集合的量子性是量子信息理论中一项重要且实用的任务。在本文中，我们通过广义α-z-相对仁义熵基于集合相干性的量词来量化量子集合的量子性。结果表明，该度量满足了量子性度量所需的直观和合意的性质，例如正性、酉不变性、任何交换性保持操作下的单调性等。讨论了我们的度量与一些现有的量子系综量子性度量之间的关系。为一些重要的集合提供了详细的例子，以说明我们的度量给出的量子性。