Efficient computation of the waiting time and fidelity in quantum repeater chains

Quantum repeaters enable surpassing the fundamental distance limit that quantum communication schemes can cover. However, realistic hardware parameters make their realization a challenge. Theoretical analysis and optimization of repeater schemes can lower the barrier for their realization. Our contributions to this are threefold. First, we provide an efficient algorithm for computing the probability distribution of the time until the first entangled state between the end nodes of a repeater chain is delivered, as well as the state's average fidelity. This improves upon the exponential runtime of existing algorithms. Next, as application, we use the algorithm for optimizing the available secret key rates for repeater schemes including a cut-off condition, which mitigates the effect of memory decoherence. We find that the use of the optimal cut-off lowers the parameter threshold for which secret key can be generated. Lastly, we use our insights gained to improve existing analytical bounds on the mean entanglement distribution rate. Our contributions thus serve as useful tools for the design and realization of long-distance quantum communication networks.