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$I_{acc}(\rho^{XA})=I(X:A)$, as the state is classical-quantum. The mutual information of product states is the sum of the mutual information of the individual states, it is additive. So since $I_{acc}(\rho^{XA})=I(X:A)$, it inherits this additive property. I will point out, however, that accessible information is not additive. It can be super-additive in ...


I'm assuming you are referring to this paper: Uncertainty, Monogamy, and Locking of Quantum Correlations. In proposition 6, it's not clear to me if they are referring to the same product state that you are considering. However, in that paper, where they mention the additivity of accessible information, along with the Holevo paper, they also cite the ...

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