  Fuchs et al. [Phys. Rev. A, 1997] suggested an optimal attack on the BB84
protocol, where the necessary and sufficient condition for optimality involves
the joint Hilbert space of the sender and the attacker. In this work, we
propose a refined optimality criteria involving the Hilbert space of the
attacker only. It reveals that the optimal (non-zero) overlaps between the
attackers post-interactions states must be equal and numerically same as the
difference between the fidelity and the disturbance at the receiving end. That
amount turns out to be same as the reduction (factor) in Bell violation when
estimated for the equivalent entanglement-based protocol. Further, a series of
necessary and sufficient conditions unveil the structure of the optimal states
which therefore are the only and all possible optimal interactions. We show
that these optimal states are same as the outputs of an optimal phase-covariant
cloner. We also demonstrate various methods to derive optimal unitary
evolutions that an eavesdropper is interested to know in order to mount an
optimal attack.
