Bell Measurement and Local Measurement in the Modified Lo-Chau Quantum Key Distribution Protocol

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