Lossy Quantum Source Coding With a Global Error Criterion Based on a Posterior Reference Map
Lossy Quantum Source Coding With a Global Error Criterion Based on a Posterior Reference Map
复制标题
基于后验参考图的全局误差准则的有损量子源编码
DOI：
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发表时间：
2023
影响因子：
2.5
通讯作者：
Touheed Anwar
中科院分区：
文献类型：
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作者：
Touheed Anwar Atif;Graduate Student Member Ieee Mohammad Aamir Sohail;F. I. S. Sandeep Pradhan;Touheed Anwar
我们考虑有损量子源编码问题，其中的任务是压缩给定的量子源低于其冯·诺依曼熵。受经典环境下速率失真和信道编码问题之间的对偶关系的启发，我们提出了一个新的有耗量子源编码问题的公式。这种表述与现有的量子速率畸变理论有两个不同之处。首先，我们要求压缩量子源的重建满足全局误差约束，而不是标准速率失真设置中使用的样本局部误差准则。其次，为了测量重建误差，我们采用后向量子信道的概念，我们称之为“后验参考映射”，而不是可观察到的失真。利用这些，我们用给定后验参考图的单字母相干信息来描述渐近性能极限。我们还开发了量子经典和经典变体的类似公式，并根据与后验参考图类似的适当定义的通道相关的单字母互信息量来表征其渐近性能极限。我们还为这三种公式提供了各种例子，并尽可能阐明它们与标准费率失真公式的联系。
We consider the lossy quantum source coding problem, where the task is to compress a given quantum source below its von Neumann entropy. Inspired by the duality connections between the rate-distortion and channel coding problems in the classical setting, we propose a new formulation for the lossy quantum source coding problem. This formulation differs from the existing quantum rate-distortion theory in two aspects. Firstly, we require that the reconstruction of the compressed quantum source fulfill a global error constraint as opposed to the sample-wise local error criterion used in the standard rate-distortion setting. Secondly, to measure the reconstruction error, instead of a distortion observable, we employ the notion of a backward quantum channel which we refer to as a “posterior reference map”. Using these, we characterize the asymptotic performance limit in terms of single-letter coherent information of the given posterior reference map. We also develop analogous formulations for the quantum-classical and classical variants and characterize their asymptotic performance limits in terms of single-letter mutual information quantities with respect to appropriately defined channels analogous to the posterior reference map. We also provide various examples for the three formulations, and shed light on their connection to the standard rate-distortion formulation wherever possible.
DOI：
10.1109/isit44484.2020.9174002
发表时间：
2020-04
期刊：
2020 IEEE International Symposium on Information Theory (ISIT)
影响因子：
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作者：
Touheed Anwar Atif;Arun Padakandla;S. Pradhan
通讯作者：
Touheed Anwar Atif;Arun Padakandla;S. Pradhan