We clarify the argument on the how (nonlocal) degenerate Bell measurement canbe replaced by local measurements in the modified Lo-Chau quantum keydistribution protocol. Discussing security criterion for users, we describe howeavesdropper's refined information on the final state is not helpful. We arguethat current discussions on the equivalence of the Bell and the localmeasurements are not clear. We show how the problem of equivalence can beresolved using the fact that eavesdropper's refined information is not helpfulfor her.
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