2017/12/12 by Atanu Acharyya, Acharyya, Atanu, Goutam Paul +1
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.1712.04475
Sequel to arXiv:1610.07148
openalex publication_date 2017/12/12 · arxiv created 2019/11/12 · arxiv updated 2019/11/13 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28
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.