On the waiting time in quantum repeaters with probabilistic entanglement swapping

TL;DR

This paper introduces an exact, systematic method using Markov chains to calculate the average waiting time and transmission rates in quantum repeaters with probabilistic entanglement swapping, improving accuracy over previous approximations.

Contribution

It provides explicit rate formulas for up to four segments, explores flexible connection schemes, and proposes a recursive approach for large systems, enhancing rate bounds and understanding of waiting time statistics.

Findings

Exact rate formulas for up to four segments with arbitrary swapping probabilities.

Finite memory times significantly affect repeater performance.

Statistical analysis shows average waiting time alone is insufficient for small probabilities.

Abstract

The standard approach to realize a quantum repeater relies upon probabilistic but heralded entangled state manipulations and the storage of quantum states while waiting for successful events. In the literature on this class of repeaters, calculating repeater rates has typically depended on approximations assuming sufficiently small probabilities. Here we propose an exact and systematic approach including an algorithm based on Markov chain theory to compute the average waiting time (and hence the transmission rates) of quantum repeaters with arbitrary numbers of links. For up to four repeater segments, we explicitly give the exact rate formulae for arbitrary entanglement swapping probabilities. Starting with three segments, we explore schemes with arbitrary (not only doubling) and dynamical (not only predetermined) connections. The effect of finite memory times is also considered and the relative influence of the classical communication (of heralded signals) is shown to grow significantly for larger probabilities. Conversely, we demonstrate that for small swapping probabilities the statistical behavior of the waiting time in a quantum repeater cannot be characterized by its average value alone and additional statistical quantifiers are needed. For large repeater systems, we propose a recursive approach based on exactly but still efficiently computable waiting times of sufficiently small sub-repeaters. This approach leads to better lower bounds on repeater rates compared to existing schemes.