Scheduling Quantum Teleportation in Noisy Memories

Quantum teleportation is a key application provided by quantum networks. Unfortunately, teleportation requires the distribution of an entangled state between two nodes which is a probabilistic process. This results in delays as the qubit to be teleported is stored in memory while it waits for an EPR pair. These delays cause fidelity loss as the qubit is continuously decohering while it is in memory. The node then has a choice of which qubit to teleport first which gives rise to a scheduling problem. This work quantifies the fidelity loss at a node in a quantum network due to storage in noisy memory platforms. We also explore the effects of different scheduling policies on fidelity. The memory platform is parameterized by decoherence rate and buffer size. We give closed-form analytical expressions for calculating the average fidelity with respect to the load, buffer size, and decoherence rate of the memory platform for different scheduling policies. We prove that serving the youngest qubits first with pushout for buffer overflow management maximizes average fidelity and is an optimal scheduling policy for exponential decay noise models. We also extend this model to calculate the average fidelity of the end-to-end entanglement produced by a quantum repeater between two nodes.