量子数据压缩和1-1编码的能量需求
Energy Requirements for Quantum Data Compression and 1-1 Coding
摘要：
通过在第二次量子化的量子数据压缩，我们提出了一个新的模型，有效地产生和使用的可变长度的代码。在这幅图中，无损数据压缩可以被看作是忠实地表示或传输包含在量子态中的经典信息所需的{ \em最小能量}。为了表示信息，我们在两种可能的内部状态（携带自由度的信息）之一中准备的一些预定义模式（即频率）中创建量子。数据压缩现在被视为这些量子的选择性湮灭，其能量有效地消散到环境中。由于环境中的能量的任何增加都与任何信息损失有着错综复杂的联系，并且受到Landauer擦除原理的影响，我们使用这一原理来区分无损和有损方案，并建议无损压缩协议的效率界限。与Bostrom和Felbinger \cite{bostroem}的工作一致，我们还证明了当使用变长码时，给定量子力学的结构，前缀或唯一可破译码的经典概念是不必要的限制，并且1-1映射是足够的。在没有这种限制的情况下，我们翻译现有的经典结果1-1编码的量子域推导出一个新的上限压缩的量子信息。最后，我们提出了一个简单的量子线路来实现我们的方案。
英文摘要：
By looking at quantum data compression in the second quantisation, we present a new model for the efficient generation and use of variable length codes. In this picture lossless data compression can be seen as the {\em minimum energy} required to faithfully represent or transmit classical information contained within a quantum state. In order to represent information we create quanta in some predefined modes (i.e. frequencies) prepared in one of two possible internal states (the information carrying degrees of freedom). Data compression is now seen as the selective annihilation of these quanta, the energy of whom is effectively dissipated into the environment. As any increase in the energy of the environment is intricately linked to any information loss and is subject to Landauer's erasure principle, we use this principle to distinguish lossless and lossy schemes and to suggest bounds on the efficiency of our lossless compression protocol. In line with the work of Boström and Felbinger \cite{bostroem}, we also show that when using variable length codes the classical notions of prefix or uniquely decipherable codes are unnecessarily restrictive given the structure of quantum mechanics and that a 1-1 mapping is sufficient. In the absence of this restraint we translate existing classical results on 1-1 coding to the quantum domain to derive a new upper bound on the compression of quantum information. Finally we present a simple quantum circuit to implement our scheme.
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