Randomness Extraction via a Quantum Generalization of the Conditional Collision Entropy
Randomness Extraction via a Quantum Generalization of the Conditional Collision Entropy
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DOI：
10.1109/tit.2019.2953155
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发表时间：
2017-03
影响因子：
2.5
通讯作者：
Yodai Watanabe
中科院分区：
文献类型：
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作者：
Yodai Watanabe
针对辅助信息的随机性提取是从给定源中提取几乎以辅助信息为条件的密钥的技术。本文提供了针对量子辅助信息的随机性提取，其可提取密钥长度由碰撞熵的量子概括给出，其平滑和条件与现有方案中的做法不同。基于碰撞熵不可次加性的事实，引入了其针对附加辅助信息的优化，并被证明是渐近最优的。那里导出的一般状态的下界被表示为两个无条件熵之间的差，并且其评估简化为两个状态的特征值问题，这两个状态是整个状态和辅助信息的边缘状态。
Randomness extraction against side information is the art of distilling from a given source a key which is almost uniform conditioned on the side information. This paper provides randomness extraction against quantum side information whose extractable key length is given by a quantum generalization of the collision entropy, which is smoothed and conditioned differently from how this is done in existing schemes. Based on the fact that the collision entropy is not subadditive, its optimization with respect to additional side information is introduced, and is shown to be asymptotically optimal. The lower bound derived there for general states is expressed as the difference between two unconditional entropies and its evaluation reduces to an eigenvalue problem of two states, which are the entire state and the marginal state of side information.