A short note on the security of Round-Robin Differential Phase-Shift QKD

Round-Robin Differential Phase-Shift (RRDPS) is a Quantum Key Distribution (QKD) scheme proposed by Sasaki, Yamamoto and Koashi in 2014 [1]. It works with highdimensional quantum digits (qudits). Its main advantage is that it tolerates more noise than qubit-based schemes while being easy to implement. The security of RRDPS has been discussed in several papers [1, 2, 3]. However, these analyses do not have the mathematical rigor that is customary in cryptology. In this short note we prove a simple result regarding the min-entropy of the distributed key; this may serve as a step towards a full security proof. 1 Preliminaries 1.1 The RRDPS scheme The dimension of the qudit space is d. The basis states are denoted as |0〉, . . . , |d− 1〉.1 Alice generates a random bitstring a ∈ {0, 1}d. She prepares the state |μ(a)〉 def = 1 √ d d−1 ∑