Optimal entanglement swapping in quantum repeaters

TL;DR

This paper formulates the optimal entanglement swapping problem in quantum repeaters as a Markov decision process, revealing that non-doubling schemes can outperform traditional methods in minimizing waiting time.

Contribution

It introduces a novel Markov decision process framework to optimize entanglement swapping, challenging the conventional doubling scheme and allowing for inclusion of classical communication effects.

Findings

Non-doubling schemes can outperform doubling in raw rate.

Optimal schemes are not restricted to power-of-two segments.

Classical communication impacts waiting time and scheme optimality.

Abstract

We formulate the problem of finding the optimal entanglement swapping scheme in a quantum repeater chain as a Markov decision process and present its solution for different repeater's sizes. Based on this, we are able to demonstrate that the commonly used "doubling" scheme for performing probabilistic entanglement swapping of probabilistically distributed entangled qubit pairs in quantum repeaters does not always produce the best possible raw rate. Focussing on this figure of merit, without considering additional probabilistic elements for error suppression such as entanglement distillation on higher "nesting levels", our approach reveals that a power-of-two number of segments has no privileged position in quantum repeater theory; the best scheme can be constructed for any number of segments. Moreover, classical communication can be included into our scheme, and we show how this influences the raw waiting time for different number of segments, confirming again the optimality of "non-doubling" in some relevant parameter regimes. Thus, our approach provides the minimal possible waiting time of quantum repeaters in a fairly general physical setting.