Efficient computation of the waiting time and fidelity in quantum repeater chains

TL;DR

This paper introduces two efficient algorithms for calculating the waiting time and fidelity of entangled pairs in quantum repeater chains, significantly improving computational efficiency and enabling analysis of large-scale quantum networks.

Contribution

The paper presents polynomial-time algorithms for analyzing quantum repeater chains, including protocols with entanglement distillation, surpassing previous exponential-time methods.

Findings

Algorithms analyze chains with thousands of segments

Faster runtime than existing methods

Able to handle refined repeater protocols

Abstract

Quantum communication enables a host of applications that cannot be achieved by classical communication means, with provably secure communication as one of the prime examples. The distance that quantum communication schemes can cover via direct communication is fundamentally limited by losses on the communication channel. By means of quantum repeaters, the reach of these schemes can be extended and chains of quantum repeaters could in principle cover arbitrarily long distances. In this work, we provide two efficient algorithms for determining the generation time and fidelity of the first generated entangled pair between the end nodes of a quantum repeater chain. The runtime of the algorithms increases polynomially with the number of segments of the chain, which improves upon the exponential runtime of existing algorithms. Our first algorithm is probabilistic and can analyze refined versions of repeater chain protocols which include intermediate entanglement distillation. Our second algorithm computes the waiting time distribution up to a pre-specified truncation time, has faster runtime than the first one and is moreover exact up to machine precision. Using our proof-of-principle implementation, we are able to analyze repeater chains of thousands of segments for some parameter regimes. The algorithms thus serve as useful tools for the analysis of large quantum repeater chain protocols and topologies of the future quantum internet.