H H. If the set of bases is large enough, then for all z there is a basis with posi- tive intrinsic information, hence the mean is also positive. Clearly, this result is stronger if the set of bases is small. Nothing is proven about the achievable size of such sets of bases, but it is conceivable that max dim A, dim B bases are always sufficient.
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Sources: Linking Classical and Quantum Key Agreement, Linking Classical and Quantum Key Agreement