We consider the most general (finite-dimensional) quantum mechanical information source, which is given by a quantum system A that is correlated with a reference system R. The task is to compress A in such a way as to reproduce the joint source state ρAR at the decoder with asymptotically high fidelity. This includes Schumacher’s original quantum source coding problem of a pure state ensemble and that of a single pure entangled state, as well as general mixed state ensembles. Here, we determine the optimal compression rate (in qubits per source system) in terms of the Koashi-Imoto decomposition of the source into a classical, a quantum, and a redundant part. The same decomposition yields the optimal rate in the presence of unlimited entanglement between compressor and decoder, and indeed the full region of feasible qubitebit rate pairs. Full version at arXiv:1912.08506 [1].
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机译：我们考虑最普通的（有限维）量子力学信息源，它是由与参考系统R相关的量子系统A给出的。任务是压缩A以便重现联合源态ρ
AR
在解码器上具有渐近高保真度。这包括舒马赫最初的纯量子态和单个纯纠缠态的量子源编码问题，以及一般的混合态集合。在这里，我们根据将源分解为经典部分，量子部分和冗余部分的Koashi-Imoto来确定最佳压缩率（以每个源系统qubits为单位）。在压缩器和解码器之间存在无限纠缠的情况下，实际上是可行的量子比特速率对的整个区域，相同的分解会产生最佳速率。完整版本位于arXiv：1912.08506 [1]。
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