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：我们重新审视了单次设定下的量子状态重分配任务，并设计了一种协议，其通信成本由与量子马尔可夫链的距离度量决定。具体而言，该距离通过量子最大相对熵和量子假设检验熵来定义。我们的结果首次在操作层面将量子状态重分配与量子马尔可夫链联系起来，可视为量子条件互信息在单次设定下可能类似物的操作性解释。该协议的通信成本低于所有先前已知方案，且在渐近条件下达到量子条件互信息的公认速率。因此，我们的工作朝着单次量子状态重分配近最优表征这一重要开放问题迈出了一步。