Quantum communication capacity transition of complex quantum networks

TL;DR

This paper investigates how the capacity of complex quantum networks transitions from near zero to linear growth as node density increases, revealing a threshold effect and independence from distance in highly connected networks.

Contribution

It identifies a critical node density threshold for capacity transition and analyzes how network topology affects quantum communication capacity.

Findings

Capacity transitions from near zero to linear with node density

Above threshold, capacity is independent of distance due to multi-path routing

In scale-free networks, capacity saturates and decays with distance

Abstract

Quantum network is the key to enable distributed quantum information processing. As the single-link communication rate decays exponentially with the distance, to enable reliable end-to-end quantum communication, the number of nodes needs to grow with the network scale. For highly connected networks, we identify a threshold transition in the capacity as the density of network nodes increases---below a critical density, the rate is almost zero, while above the threshold the rate increases linearly with the density. Surprisingly, above the threshold the typical communication capacity between two nodes is independent of the distance between them, due to multi-path routing enabled by the quantum network. In contrast, for less connected networks such as scale-free networks, the end-to-end capacity saturates to constants as the number of nodes increases, and always decays with the distance. Our results are based on capacity evaluations, therefore the minimum density requirement for an appreciable capacity applies to any general protocols of quantum networks.