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On this page, it is stated that the Holevo quantity is an upper bound to the accessible information of a quantum state. In the scenario where Alice encodes classical information into a quantum state and sends it to Bob, the accessible information is the maximum of the mutual information between Alice and Bob's registers over all possible measurements that Bob makes.

On the other hand, the classical capacity of a quantum channel also looks at the mutual information between Alice and Bob. The maximization of this mutual information is the Holevo quantity.

I do not understand the difference in the two settings. In particular, why is the Holevo quantity only an upper bound in the first linked page but is equal to the maximum mutual information in the second linked page?

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