Sharma Kunal, Wakakuwa Eyuri, Wilde Mark M
Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA.
Graduate School of Informatics and Engineering, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo, 182-8585, Japan.
Phys Rev Lett. 2020 Feb 7;124(5):050503. doi: 10.1103/PhysRevLett.124.050503.
Suppose that Alice and Bob are located in distant laboratories, which are connected by an ideal quantum channel. Suppose further that they share many copies of a quantum state ρ_{ABE}, such that Alice possesses the A systems and Bob the BE systems. In our model, there is an identifiable part of Bob's laboratory that is insecure: a third party named Eve has infiltrated Bob's laboratory and gained control of the E systems. Alice, knowing this, would like use their shared state and the ideal quantum channel to communicate a message in such a way that Bob, who has access to the whole of his laboratory (BE systems), can decode it, while Eve, who has access only to a sector of Bob's laboratory (E systems) and the ideal quantum channel connecting Alice to Bob, cannot learn anything about Alice's transmitted message. We call this task the conditional one-time pad, and in this Letter, we prove that the optimal rate of secret communication for this task is equal to the conditional quantum mutual information I(A;B|E) of their shared state. We thus give the conditional quantum mutual information an operational meaning that is different from those given in prior works, via state redistribution, conditional erasure, or state deconstruction. We also generalize the model and method in several ways, one of which is a secret-sharing task, i.e., the case in which Alice's message should be secure from someone possessing only the AB or AE systems, but should be decodable by someone possessing all systems A, B, and E.
假设爱丽丝和鲍勃位于相距遥远的实验室中，这两个实验室通过一条理想量子信道相连。进一步假设他们共享许多量子态ρ_{ABE}的副本，使得爱丽丝拥有A系统，鲍勃拥有BE系统。在我们的模型中，鲍勃的实验室存在一个可识别的不安全部分：一个名为伊芙的第三方潜入了鲍勃的实验室并控制了E系统。爱丽丝知道这一情况，她想用他们共享的量子态和理想量子信道来传递一条信息，使得能够访问其整个实验室（BE系统）的鲍勃可以解码该信息，而只能访问鲍勃实验室的一个部分（E系统）以及连接爱丽丝和鲍勃的理想量子信道的伊芙，无法得知爱丽丝所传递信息的任何内容。我们将此任务称为条件一次性密码本，在本信函中，我们证明了此任务的最优秘密通信速率等于他们共享量子态的条件量子互信息I(A;B|E)。因此，我们通过状态再分配、条件擦除或状态解构，赋予了条件量子互信息一种与先前工作中所赋予的不同的操作意义。我们还在几个方面对模型和方法进行了推广，其中之一是一个秘密共享任务，即爱丽丝的信息对于仅拥有AB或AE系统的人而言应该是安全的，但对于拥有所有系统A、B和E的人而言应该是可解码的。
