In this paper we consider the compression of asymptotically many i.i.d. copies of ensembles of mixed quantum states where 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：本文考虑渐近独立同分布混合量子态系综的压缩问题，其中编码器可获取边信息系统。性能指标为单副本或局部误差准则。率失真理论研究压缩率与单副本误差之间的权衡关系。最优权衡可通过率失真函数表征，即给定失真下的最优压缩率。本文推导了混合态压缩的率失真函数。纠缠辅助与无辅助场景下的率失真函数分别表示为单字母互信息量和正则化纠缠纯化量。对于同时考虑通信与纠缠消耗的一般设置，我们给出了完整的量子比特-纠缠率区域。根据边信息系统的结构，我们的压缩方案涵盖盲压缩模型、可视压缩模型及介于两者之间的其他模型。