Asymptotic Analysis of a Three State Quantum Cryptographic Protocol

TL;DR

This paper analyzes a three-state quantum key distribution protocol, deriving a new lower bound on its key rate and demonstrating its robustness up to an 11% error rate, comparable to the four-state BB84 protocol.

Contribution

It introduces a novel lower bound on the key rate for a three-state QKD protocol and utilizes mismatched measurements to enhance channel estimation.

Findings

Key rate remains positive up to 11% error rate

New lower bound on the key rate derived

Mismatched measurements improve channel estimation

Abstract

In this paper we consider a three-state variant of the BB84 quantum key distribution (QKD) protocol. We derive a new lower-bound on the key rate of this protocol in the asymptotic scenario and use mismatched measurement outcomes to improve the channel estimation. Our new key rate bound remains positive up to an error rate of $11\%$, exactly that achieved by the four-state BB84 protocol.