Quantum aggregation with temporal delay

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 difference in 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. Furthermore, 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.