We establish a coding theorem for rate-limited quantum-classical optimal transport systems with limited classical common randomness. This theorem characterizes the rate region of measurement protocols on a product source state for faithful construction of a given destination state while maintaining the source-destination distortion below a prescribed threshold with respect to a general distortion observable. It also provides a solution to the problem of rate-limited optimal transport, which aims to find the optimal cost of transforming a source quantum state to a destination state via an entanglement-breaking channel with a limited communication rate. The coding theorem is further extended to cover Bosonic continuous-variable quantum systems. The analytical evaluation is performed for the case of a qubit measurement system with unlimited common randomness.

翻译：我们建立了在有限经典公共随机性下码率受限的量子-经典最优输运系统的编码定理。该定理刻画了通过测量协议对乘积源态进行忠实构造目标态时的码率区域，同时确保源-目标失真相对于一般失真可观测量低于指定阈值。该定理还解决了码率受限的最优输运问题，即通过具有有限通信速率的纠缠破坏信道将源量子态变换至目标态的最优成本。该编码定理进一步扩展至涵盖玻色连续变量量子系统。针对具有无限公共随机性的量子比特测量系统进行了解析评估。