A complete characterization of the optimal unitary attacks in quantum cryptography with a refined optimality criteria involving the attacker’s Hilbert space only

Fuchs et al. (Phys Rev A 56:1163, 1997, https://doi.org/10.1103/PhysRevA.56.1163 ) suggested an optimal attack on the BB84 protocol, where necessary and sufficient condition for optimality involves joint Hilbert space of sender attacker. In this work, we propose a refined criteria involving attacker only. It reveals that (non-zero) overlaps between attackers post-interactions states must be equal numerically same as difference fidelity disturbance at receiving end. That amount turns out to reduction (factor) in Bell violation when estimated equivalent entanglement-based protocol. Further, series conditions unveil structure which therefore are only all possible interactions. These outputs phase-covariant cloner. We also demonstrate various methods derive unitary evolutions eavesdropper is interested know order mount attack. The final key-rate computed plotted well.