Horodecki Michał, Oppenheim Jonathan, Winter Andreas
Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland.
Nature. 2005 Aug 4;436(7051):673-6. doi: 10.1038/nature03909.
Information--be it classical or quantum--is measured by the amount of communication needed to convey it. In the classical case, if the receiver has some prior information about the messages being conveyed, less communication is needed. Here we explore the concept of prior quantum information: given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the partial information one system needs, conditioned on its prior information. We find that it is given by the conditional entropy--a quantity that was known previously, but lacked an operational meaning. In the classical case, partial information must always be positive, but we find that in the quantum world this physical quantity can be negative. If the partial information is positive, its sender needs to communicate this number of quantum bits to the receiver; if it is negative, then sender and receiver instead gain the corresponding potential for future quantum communication. We introduce a protocol that we term 'quantum state merging' which optimally transfers partial information. We show how it enables a systematic understanding of quantum network theory, and discuss several important applications including distributed compression, noiseless coding with side information, multiple access channels and assisted entanglement distillation.
信息——无论是经典信息还是量子信息——都是通过传达它所需的通信量来衡量的。在经典情况下，如果接收者对正在传达的消息有一些先验信息，那么所需的通信量就会减少。在这里，我们探讨先验量子信息的概念：给定一个分布在两个系统上的未知量子态，我们确定将完整状态转移到一个系统需要多少量子通信。这种通信量衡量了一个系统基于其先验信息所需的部分信息。我们发现它由条件熵给出——这是一个之前就已知的量，但缺乏操作意义。在经典情况下，部分信息必须始终为正，但我们发现在量子世界中这个物理量可以为负。如果部分信息为正，其发送者需要将这个量子比特数传达给接收者；如果为负，那么发送者和接收者反而获得了未来量子通信的相应潜力。我们引入了一种我们称为“量子态合并”的协议，它能最优地转移部分信息。我们展示了它如何使我们能够系统地理解量子网络理论，并讨论了几个重要应用，包括分布式压缩、有边信息的无噪声编码、多址信道和辅助纠缠蒸馏。
