The Classical Capacity of Quantum Jackson Networks with Waiting Time-Dependent Erasures

TL;DR

This paper investigates the maximum classical communication capacity of quantum networks with queues, focusing on how waiting time-dependent erasures due to decoherence affect information transfer, and provides explicit capacity formulas for simple network topologies.

Contribution

It introduces explicit capacity expressions for quantum queue-networks with waiting time-dependent erasures and characterizes the capacity of general quantum Jackson networks, including optimal routing strategies.

Findings

Explicit capacity formulas for tandem and parallel queue-channels.

Capacity characterization for general quantum Jackson networks.

Optimal routing and pumping rates to maximize capacity.

Abstract

We study the fundamental limits of classical communication using quantum states that decohere as they traverse through a network of queues. We consider a network of Markovian queues, known as a Jackson network, with a single source or multiple sources and a single destination. Qubits are communicated through this network with inevitable buffering at intermediate nodes. We model each node as a `queue-channel,' wherein as the qubits wait in buffer, they continue to interact with the environment and suffer a waiting time-dependent noise. Focusing on erasures, we first obtain explicit classical capacity expressions for simple topologies such as tandem queue-channel and parallel queue-channel. Using these as building blocks, we characterize the classical capacity of a general quantum Jackson network with waiting time-dependent erasures. Throughout, we study two types of quantum networks, namely, (i) Repeater-assisted and (ii) Repeater-less. We also obtain optimal pumping rates and routing probabilities to maximize capacity in simple topologies. More broadly, our work quantifies the impact of delay-induced decoherence on the fundamental limits of classical communication over quantum networks.