  Advanced quantum networking systems rely on efficient quantum error
correction codes for their optimal realization. The rate at which the encoded
information is transmitted is a fundamental limit that affects the performance
of such systems. Quantum aggregation allows one to increase the transmission
rate by adding multiple paths connecting two distant users. Aggregating
channels of different paths allows more users to simultaneously exchange the
encoded information. Recent work has shown that quantum aggregation can also
reduce the number of physical resources of an error correction code when it is
combined with the quantum multiplexing technique. However, the different
channel lengths across the various paths means some of the encoded quantum
information will arrive earlier than others and it must be stored in quantum
memories. The information stored will then deteriorate due to decoherence
processes leading to detrimental effects for the fidelity of the final quantum
state. Here, we explore the effects of a depolarization channel that occurs for
the quantum Reed-Solomon code when quantum aggregation involving different
channel lengths is used. We determine the best distribution of resources among
the various channels connecting two remote users. Further we estimate the
coherence time required to achieve a certain fidelity. Our results will have a
significant impact on the ways physical resources are distributed across a
quantum network.
