For some reason, I wanted to know the following fact at some point.

Let be an ensemble of states of a bipartite system . For the Holevo information, we have where is the expected value of the quantum mutual information .

Since the Holevo information gives an upper bound for the mutual information between the random variable and the outcome of any measurement that can be made on the received state, setting we see that may be meaningfully taken as an upper bound for the amount of hidden information.

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