Efficient quantum key distribution with trines of reference-frame-free qubits

TL;DR

This paper introduces a rotationally-invariant quantum key distribution scheme using orthogonal qubit trines, achieving high key rates and security against noise, with practical advantages over standard methods.

Contribution

It presents a novel reference-frame-free QKD protocol with improved key efficiency and security analysis, utilizing mixed states of three qubits and two-way communication.

Findings

Achieves 0.573 key bits per trine state in noiseless channels.

Exceeds standard trine schemes in key yield.

Secure below noise threshold of 0.197 epsilon.

Abstract

We propose a rotationally-invariant quantum key distribution scheme that uses a pair of orthogonal qubit trines, realized as mixed states of three physical qubits. The measurement outcomes do not depend on how Alice and Bob choose their individual reference frames. The efficient key generation by two-way communication produces two independent raw keys, a bit key and a trit key. For a noiseless channel, Alice and Bob get a total of 0.573 key bits per trine state sent (98% of the Shannon limit). This exceeds by a considerable amount the yield of standard trine schemes, which ideally attain half a key bit per trine state. Eavesdropping introduces an $\epsilon$-fraction of unbiased noise, ensured by twirling if necessary. The security analysis reveals an asymmetry in Eve's conditioned ancillas for Alice and Bob resulting from their inequivalent roles in the key generation. Upon simplifying the analysis by a plausible symmetry assumption, we find that a secret key can be generated if the noise is below the threshold set by $\epsilon = 0.197$.