The transmission of classical information over a classical channel gave rise to the classical capacity theorem with the optimal rate in terms of the classical mutual information. Despite classical information being a subset of quantum information, the rate of the quantum capacity problem is expressed in terms of the coherent information, which does not mathematically generalize the classical mutual information. Additionally, there are multiple capacity theorems with distinct formulas when dealing with transmitting information over a noisy quantum channel. This leads to the question of what constitutes a mathematically accurate quantum generalization of classical mutual information and whether there exists a quantum task that directly extends the classical capacity problem. In this paper, we address these inquiries by introducing a quantity called the generalized information, which serves as a mathematical extension encompassing both classical mutual information and coherent information. We define a transmission task, which includes as specific instances both classical information and quantum information capacity problems, and show that the transmission capacity of this task is characterized by the generalized information.

翻译：经典信息通过经典通道的传输催生了经典容量定理，其最优速率由经典互信息表达。尽管经典信息是量子信息的子集，但量子容量问题的速率却由相干信息表示，而相干信息在数学上并非经典互信息的推广。此外，在通过嘈杂量子通道传输信息时，存在多种具有不同公式的容量定理。这引发了一个问题：什么是经典互信息在数学上准确的量子推广？是否存在直接扩展经典容量问题的量子任务？在本文中，我们通过引入一个称为广义信息的量来回应这些探究，该量作为数学扩展涵盖了经典互信息和相干信息两者。我们定义了一个传输任务，该任务将经典信息容量问题和量子信息容量问题作为具体实例包括在内，并证明了该任务的传输容量由广义信息刻画。