Tradeoff relations between accessible information, informational power, and purity
Tradeoff relations between accessible information, informational power, and purity
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可获取信息、信息力量和纯度之间的权衡关系
DOI：
10.1109/tit.2018.2874989
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发表时间：
2018
影响因子：
2.5
通讯作者：
Buscemi Francesco
中科院分区：
文献类型：
--
作者：
Dall'Arno Michele;Buscemi Francesco
可访问信息和信息功率分别量化了可以从量子系综和通过量子测量提取的最大信息量。在这里，我们研究了可访问信息（分别是信息能力）和整体状态纯度（分别是测量元素）之间的权衡。在任何给定的纯度下限下，1）我们计算最小信息功率并表明它是通过去极化均匀分布测量获得的； 2）我们给出可访问信息的下限。在任何给定的纯度上限下，1）我们计算最大可访问信息，并表明它是通过具有最多两个不同的非空特征值的成对交换状态的集合来获得的； 2）我们给出最大信息能力的下限。作为推论，目前的结果为 Jozsa-Robb-Wootters 下界与可访问信息的紧密性提供了新颖的充分条件。
The accessible information and the informational power quantify the maximum amount of information that can be extracted from a quantum ensemble and by a quantum measurement, respectively. Here, we investigate the tradeoff between the accessible information (informational power, respectively) and the purity of the states of the ensemble (the elements of the measurement, respectively). Under any given lower bound on the purity, 1) we compute the minimum informational power and show that it is attained by the depolarized uniformly-distributed measurement; and 2) we give a lower bound on the accessible information. Under any given upper bound on the purity, 1) we compute the maximum accessible information and show that it is attained by an ensemble of pairwise commuting states with at most two distinct non-null eigenvalues; and 2) we give a lower bound on the maximum informational power. The present results provide, as a corollary, novel sufficient conditions for the tightness of the Jozsa-Robb-Wootters lower bound to the accessible information.