Revisiting optimal eavesdropping in quantum cryptography: Optimal interaction is unique up to rotation of the underlying basis

TL;DR

This paper resolves a long-standing open problem by proving the uniqueness of optimal eavesdropping interactions in the BB84 quantum cryptography protocol, up to a rotation of the basis, thereby clarifying the nature of optimal attacks.

Contribution

The paper proves the uniqueness of the optimal eavesdropping interaction in BB84, up to basis rotation, extending and clarifying previous results by Fuchs et al.

Findings

Optimal interaction is unique up to rotation of the basis.

The specific interaction by Fuchs et al. is a special case of the derived form.

Resolved a two-decade-old open problem in quantum cryptography.

Abstract

A general framework of optimal eavesdropping on BB84 protocol was provided by Fuchs et al. [Phys. Rev. A, 1997]. An upper bound on mutual information was derived, which could be achieved by a specific type of interaction and the corresponding measurement. However, uniqueness of optimal interaction was posed as an unsolved problem there and it has remained open for almost two decades now. In this paper, we solve this open problem and establish the uniqueness of optimal interaction up to rotation. The specific choice of optimal interaction by Fuchs et al. is shown to be a special case of the form derived in our work.