Compatible Information as a Natural Information Measure of a Quantum Channel

As a natural quantitative characteristic of mutual information contained in two compatible sets of quantum states considered as input and output, we introduce the Shannon amount of information corresponding to two independent general measurements of all possible quantum states of the input and output. We analyze the physical content of this information measure and its relation to other measures such as the Holevo information and coherent information. In an example of two two-level systems, the most important features of compatible information in the absence and presence of selection for measured states are revealed and discussed.