We show that there is a tradeoff between the useful key distribution bit rateand the total length of deployed fiber in tree-type passive optical networksfor BB84 quantum key distribution applications. A two stage splittingarchitecture where one splitting is carried in the central office and a secondin the outside plant and figure of merit to account for the tradeoff areproposed. We find that there is an optimum solution for the splitting ratios ofboth stages in the case of Photon Number Splitting (PNS) attacks and DecoyState transmission. We then analyze the effects of the different relevantphysical parameters of the PON on the optimum solution.
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