Exploring the Limitations of Quantum Networking through Butterfly‐Based Networks

Abstract

AbstractThe classical and quantum networking regimes of the butterfly network and a group of larger networks constructed with butterfly network blocks are investigated. By considering simultaneous multicasts from a set of senders to a set of receivers, the corresponding rates for transmitting classical and quantum information through the networks are analyzed. More precisely, achievable rates (i.e., lower bounds) for classical communication are compared 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, a range is observed over which the classical rate non‐trivially exceeds the quantum capacity. It is found 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). The 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,” some guidance on how quantum networks should be built is also provided.