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We study the fundamental limits of classical communication using quantumstates that decohere as they traverse through a network of queues. We considera network of Markovian queues, known as a Jackson network, with a single sourceor multiple sources and a single destination. Qubits are communicated throughthis network with inevitable buffering at intermediate nodes. We model eachnode as a `queue-channel,' wherein as the qubits wait in buffer, they continueto interact with the environment and suffer a waiting time-dependent noise.Focusing on erasures, we first obtain explicit classical capacity expressionsfor simple topologies such as tandem queue-channel and parallel queue-channel.Using these as building blocks, we characterize the classical capacity of ageneral 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 ratesand routing probabilities to maximize capacity in simple topologies. Morebroadly, our work quantifies the impact of delay-induced decoherence on thefundamental limits of classical communication over quantum networks.

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