Simple Error Scattering Model for improved Information Reconciliation

TL;DR

This paper introduces a simple error scattering model for quantum key distribution that provides analytical expressions to improve the efficiency of information reconciliation, addressing key rate limitations.

Contribution

It proposes a new, straightforward error scattering model with closed-form formulas for error detection probabilities, aiding more efficient quantum key distribution processes.

Findings

Derived closed-form expressions for error detection probabilities.

Supported hypotheses on error distribution with statistical analysis.

Potential to enhance key reconciliation efficiency.

Abstract

Implementations of quantum key distribution as available nowadays suffer from inefficiencies due to post processing of the raw key that severely cuts down the final secure key rate. We present a simple model for the error scattering across the raw key and derive "closed form" expressions for the probability of a parity check failure, or experiencing more than some fixed number of errors. Our results can serve for improvement for key establishment, as information reconciliation via interactive error correction and privacy amplification rests on mostly unproven assumptions. We support those hypotheses on statistical grounds.