We consider a variation of the well-studied quantum state redistribution task, in which the starting state is known only to the receiver Bob and not to the sender Alice. We refer to this as quantum state redistribution with a one-sided promise. In addition, we consider communication from Alice to Bob over a noisy channel $\mathcal {N}$ , instead of the noiseless channel, as is usually considered in state redistribution. We take a natural approach towards the solution of this problem where we “embed” the promise as part of the state and then invoke known protocols for quantum state redistribution composed with known protocols for transfer of quantum information over noisy channels. Using our approach, we are able to reproduce the Alpha-bit capacities with or without entanglement assistance in Hayden and Penington, using known protocols for quantum state redistribution and quantum communication over noisy channels. Furthermore, we generalize the entanglement assisted classical Alpha-bit capacity, showing that any quantum state redistribution protocol can be used as a black box to simulate classical communication.

中文翻译：

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带有承诺和 Alpha 位的嘈杂量子态再分配

我们考虑了经过充分研究的量子状态重新分配任务的一种变体，其中起始状态只有接收者 Bob 知道，而发送者 Alice 不知道。我们将其称为具有片面承诺的量子状态重新分配。此外，我们考虑了从 Alice 到 Bob 的通信通过噪声通道 $\mathcal {N}$ ，而不是状态重新分配中通常考虑的无噪声通道。我们采取一种自然的方法来解决这个问题，我们将承诺“嵌入”为状态的一部分，然后调用已知的量子状态重新分配协议，这些协议由已知的协议组成，用于在嘈杂的信道上传输量子信息。使用我们的方法，我们能够在海登和佩宁顿有或没有纠缠辅助的情况下重现 Alpha 位容量，使用已知的协议进行量子状态重新分配和噪声信道上的量子通信。此外，我们概括了纠缠辅助的经典 Alpha 位容量，表明任何量子状态重新分配协议都可以用作黑匣子来模拟经典通信。