We revisit the task of quantum state redistribution in the one-shot setting, and design a protocol for this task with communication cost in terms of a measure of distance from quantum Markov chains. More precisely, the distance is defined in terms of quantum max-relative entropy and quantum hypothesis testing entropy. Our result is the first to operationally connect quantum state redistribution and quantum Markov chains, and can be interpreted as an operational interpretation for a possible one-shot analogue of quantum conditional mutual information. The communication cost of our protocol is lower than all previously known ones and asymptotically achieves the well-known rate of quantum conditional mutual information. Thus, our work takes a step towards the important open question of near-optimal characterization of the one-shot quantum state redistribution.
翻译:我们重新审视了在一发式环境下量子状态再分配的任务,并为这项任务设计了一个协议,以与量子马尔科夫链的距离测量通信成本计算。更准确地说,距离的定义是量子最大反动灵敏度和量子假设测试酶。我们的结果是第一个将量子状态再分配和量子马尔科夫链在操作上连接起来,并可以被解释为对量子有条件的相互信息可能的一次性模拟的操作解释。我们协议的通信成本比所有已知的通信成本低,并且无异性地实现了已知的量子有条件的相互信息率。 因此,我们的工作朝着一个重要的开放问题迈出了一步,即一发式量子量子再分配的近最佳定性问题。