Security proof for Round Robin Differential Phase Shift QKD

TL;DR

This paper provides a rigorous security proof for the Round Robin Differential Phase Shift QKD protocol, establishing tight bounds on privacy amplification and analyzing Eve's optimal attack strategies.

Contribution

It introduces a security proof for the protocol, including an EPR variant and tight bounds on privacy amplification for finite and asymptotic key sizes.

Findings

Derived a tight bound on privacy amplification required.

Identified Eve's optimal coupling strategy under error constraints.

Provided sharper asymptotic security bounds than previous work.

Abstract

We give a security proof of the `Round Robin Differential Phase Shift' Quantum Key Distribution scheme, and we give a tight bound on the required amount of privacy amplification. 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. As a function of beta we derive, for finite key size, the trace distance between the real state and a state in which no leakage exists. For asymptotic key size we obtain a bound on the trace distance by computing the von Neumann entropy. Our asymptotic result for the privacy amplification is sharper than existing bounds.