Paper 2017/830

Security proof for Round Robin Differential Phase Shift QKD

Daan Leermakers and Boris Skoric

Abstract

We give the first information-theoretic security proof of the `Round Robin Differential Phase Shift' Quantum Key Distribution scheme. Our proof consists of the following steps. We construct an EPR variant of the scheme. We identify Eve's optimal way of coupling an ancilla to an EPR qudit pair under the constraint that the bit error rate between Alice and Bob should not exceed a value~$\beta$. We determine, as a function of $\beta$, which POVM measurement on the ancilla Eve has to perform in order to learn as much as possible about Alice's bit. It turns out that Eve's potential knowledge is much smaller than suggested in existing security analyses.