Exploring the limitations of quantum networking through butterfly-based networks

TL;DR

This paper analyzes the limitations of quantum networks using butterfly network structures, comparing classical and quantum communication rates to identify scenarios where classical communication outperforms quantum capacity.

Contribution

It provides a quantitative analysis of classical versus quantum communication rates in butterfly networks, highlighting configurations that are disadvantageous for quantum networking.

Findings

Classical rates can exceed quantum capacity in certain network configurations.

Adding butterfly blocks can increase the gap between classical and quantum transmission.

Identifies network scenarios where quantum communication is significantly limited.

Abstract

We investigate the classical and quantum networking regimes of the butterfly network and a group of larger networks constructed with butterfly network blocks. By considering simultaneous multicasts from a set of senders to a set of receivers, we analyze the corresponding rates for transmitting classical and quantum information through the networks. More precisely, we compare achievable rates (i.e., lower bounds) for classical communication with upper bounds for quantum communication, quantifying the performance gap between the rates for networks connected by identity, depolarizing and erasure channels. For each network considered, we observe a range over which the classical rate non-trivially exceeds the quantum capacity. We find that, by adding butterfly blocks in parallel, the difference between transmitted bits and qubits can be increased up to one extra bit per receiver in the case of perfect transmission (identity channels). Our aim is to provide a quantitative analysis of those network configurations which are particularly disadvantageous for quantum networking, when compared to classical communication. By clarifying the performance of these 'negative cases', we also provide some guidance on how quantum networks should be built.