Simple efficient decoders for quantum key distribution over quantum repeaters with encoding

TL;DR

This paper introduces simplified decoders for quantum key distribution over quantum repeaters with encoding, demonstrating improved performance and easier implementation, especially with three-qubit repetition codes, under realistic error conditions.

Contribution

Proposes two new decoder structures for encoded quantum repeaters that enhance performance and simplify implementation by removing two-qubit gates, with analysis of their robustness and practical regimes.

Findings

Encoded repeaters can outperform probabilistic ones in certain regimes.

Simplified decoders remove complex two-qubit gates, easing implementation.

Three-qubit repetition codes show practical advantages in feasible operational regimes.

Abstract

We study the implementation of quantum key distribution (QKD) systems over quantum repeater infrastructures. We particularly consider quantum repeaters with encoding and compare them with probabilistic quantum repeaters. To that end, we propose two decoder structures for encoded repeaters that not only improve system performance but also make the implementation aspects easier by removing two-qubit gates from the QKD decoder. By developing several scalable numerical and analytical techniques, we then identify the resilience of the setup to various sources of error in gates, measurement modules, and initialization of the setup. We apply our techniques to three- and five-qubit repetition codes and obtain the normalized secret key generation rate per memory per second for encoded and probabilistic quantum repeaters. We quantify the regimes of operation, where one class of repeater outperforms the other, and find that there are feasible regimes of operation where encoded repeaters -- based on simple three-qubit repetition codes -- could offer practical advantages.