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Smooth Entropy Bounds on One-Shot Quantum State Redistribution

机译：一射量子态重新分布的光滑熵界

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摘要

In quantum state redistribution as introduced by Luo and Devetak and Devetak and Yard, there are four systems of interest: the system held by Alice; the system held by Bob; the system that is to be transmitted from Alice to Bob; and the system that holds a purification of the state in the registers. We give upper and lower bounds on the amount of quantum communication and entanglement required to perform the task of quantum state redistribution in a one-shot setting. Our bounds are in terms of the smooth conditional min- and max-entropy, and the smooth max-information. The protocol for the upper bound has a clear structure, building on the work of Oppenheim: it decomposes the quantum state redistribution task into two simpler coherent state merging tasks by introducing a coherent relay. In the independent and identical (i.i.d.) asymptotic limit our bounds for the quantum communication cost converge to the quantum conditional mutual information , and our bounds for the total cost converge to the conditional entropy . This yields an alternative proof of optimality of these rates for quantum state redistribution in the i.i.d. asymptotic limit. In particular, we obtain a strong converse for quantum state redistribution, which even holds when allowing for feedback.
机译：在Luo和Devetak以及Devetak和Yard提出的量子态重新分配中，有四个感兴趣的系统：爱丽丝持有的系统；鲍勃拥有的系统；从爱丽丝传输到鲍勃的系统；以及在寄存器中保持状态净化的系统。我们给出了在单次设置中执行量子态重新分布任务所需的量子通信和纠缠量的上限和下限。我们的边界取决于光滑的条件最小熵和最大熵以及光滑的最大信息。上限协议以Oppenheim的工作为基础，结构清晰：通过引入相干中继，将量子态重新分布任务分解为两个更简单的相干态合并任务。在独立且相同的（i.d.d）渐近极限中，我们的量子通信成本边界收敛于量子条件互信息，而我们的总成本边界收敛于条件熵。这为i.i.d中的量子态重新分布提供了这些速率的最优性的另一种证明。渐近极限。尤其是，我们获得了量子态重新分布的强烈反面，甚至在允许反馈时也是如此。

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