This paper is concerned with quantum data compression of asymptotically many independent and identically distributed copies of ensembles of mixed quantum states. The encoder has access to a side information system. The figure of merit is per-copy or local error criterion. Rate-distortion theory studies the trade-off between the compression rate and the per-copy error. The optimal trade-off can be characterized by the rate-distortion function, which is the best rate given a certain distortion. In this paper, we derive the rate-distortion function of mixed-state compression. The rate-distortion functions in the entanglement-assisted and unassisted scenarios are in terms of a single-letter mutual information quantity and the regularized entanglement of purification, respectively. For the general setting where the consumption of both communication and entanglement are considered, we present the full qubit-entanglement rate region. Our compression scheme covers both blind and visible compression models (and other models in between) depending on the structure of the side information system.

翻译：本文研究渐近多个独立同分布混合量子态系综的量子数据压缩问题。编码器可访问边信息系统。评价指标采用每拷贝或局部误差准则。率失真理论研究压缩率与每拷贝误差之间的权衡关系。最优权衡可通过率失真函数表征，该函数表示给定特定失真条件下的最佳速率。本文推导了混合态压缩的率失真函数：纠缠辅助场景下的率失真函数表现为单字母互信息量，而无辅助场景则表现为正则化纯化纠缠度。针对同时考虑通信消耗与纠缠消耗的一般设置，我们给出了完整的量子比特-纠缠速率区域。根据边信息系统的结构差异，我们的压缩方案涵盖了盲压缩与可视压缩模型（及介于两者之间的其他模型）。