单次量子态合并
Single-shot Quantum State Merging
摘要：
我们考虑一个未知的量子态共享双方，爱丽丝和鲍勃，并询问需要多少量子通信传输完整的状态鲍勃。这个问题被称为状态合并，并且在[Horodecki等人，Nature，436，673（2005）]。已经表明，对于自由经典通信，需要从Alice发送到Bob的最小量子比特数由条件冯诺伊曼熵给出。然而，这个结果只在渐近意义上成立（在这个意义上，爱丽丝和鲍勃最初共享状态的许多相同副本），并且不清楚合并单个副本需要多少量子通信。我们证明了实现这种单次状态合并所需的最小量子通信量是通过减去Alice在环境条件下的光滑条件最小熵来给出的。这就给光滑条件最小熵赋予了操作意义。
英文摘要：
We consider an unknown quantum state shared between two parties, Alice and Bob, and ask how much quantum communication is needed to transfer the full state to Bob. This problem is known as state merging and was introduced in [Horodecki et al., Nature, 436, 673 (2005)]. It has been shown that for free classical communication the minimal number of quantum bits that need to be sent from Alice to Bob is given by the conditional von Neumann entropy. However this result only holds asymptotically (in the sense that Alice and Bob share initially many identical copies of the state) and it was unclear how much quantum communication is necessary to merge a single copy. We show that the minimal amount of quantum communication needed to achieve this single-shot state merging is given by minus the smooth conditional min-entropy of Alice conditioned on the environment. This gives an operational meaning to the smooth conditional min-entropy.
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