Symmetry-protected privacy: beating the rate-distance linear bound over a noisy channel

TL;DR

This paper introduces a symmetry-based security proof for quantum key distribution that overcomes the traditional rate-distance linear bound, allowing secure communication even with high error rates and practical noise conditions.

Contribution

It presents a novel symmetry-based security proof that decouples privacy from channel disturbance, enabling quantum key distribution beyond previous error rate limitations.

Findings

Breaks the linear bound with a 13% error rate in simulation

Allows positive key rates with up to 50% bit error rate

Finite-data analysis shows feasibility with 10^12 data samples

Abstract

There are two main factors limiting the performance of quantum key distribution --- channel transmission loss and noise. Previously, a linear bound was believed to put an upper limit on the rate-transmittance performance. Remarkably, the recently proposed twin-field and phase-matching quantum key distribution schemes have been proven to overcome the linear bound. In practice, due to the intractable phase fluctuation of optical signals in transmission, these schemes suffer from large error rates, which renders the experimental realization extremely challenging. Here, we close this gap by proving the security based on a different principle --- encoding symmetry. With the symmetry-based security proof, we can decouple the privacy from the channel disturbance, and eventually remove the limitation of secure key distribution on bit error rates. That is, the phase-matching scheme can yield positive key rates even with high bit error rates up to 50%. In simulation, with typical experimental parameters, the key rate is able to break the linear bound with an error rate of 13%. Meanwhile, we provide a finite-data size analysis for the scheme, which can break the bound with a reasonable data size of $10^{12}$. Encouraged by high loss- and error-tolerance, we expect the approach based on symmetry-protected privacy will provide a new insight to the security of quantum key distribution.