In classical information theory, uncommon information refers to the amount of information that is not shared between two messages, and it admits an operational interpretation as the minimum communication cost required to exchange the messages. Extending this notion to the quantum setting, quantum uncommon information is defined as the amount of quantum information necessary to exchange two quantum states. While the value of uncommon information can be computed exactly in the classical case, no direct method is currently known for calculating its quantum analogue. Prior work has primarily focused on deriving upper and lower bounds for quantum uncommon information. In this work, we propose a new approach for estimating these bounds by utilizing the quantum Donsker-Varadhan representation and implementing a gradient-based optimization method. Our results suggest a pathway toward efficient approximation of quantum uncommon information using variational techniques grounded in quantum neural architectures.

翻译：在经典信息论中，非共有信息指两个消息之间不共享的信息量，其操作解释可理解为交换消息所需的最小通信成本。将此概念推广至量子领域，量子非共有信息被定义为交换两个量子态所需的量子信息量。尽管在经典情形下非共有信息的值可被精确计算，目前尚无直接方法可用于计算其量子对应量。先前研究主要集中于推导量子非共有信息的上界与下界。本研究提出一种新方法，通过利用量子唐斯克-瓦拉丹表示并实施基于梯度的优化算法来估计这些界。我们的研究结果为基于量子神经架构的变分技术实现量子非共有信息的高效近似指明了一条可行路径。