The PLOB-bound ("Fundamental Limits of Repeaterless Quantum Communications") gives an asymptotic upper bound on the secret-key rate per used lossy bosonic channel. However, I'm not sure how to count the number of used channels in a physical implementation.

For example, let's assume that I use the BB84 protocol encoded in the polarization degrees of freedom of a single photon pulse. One could think that one uses two lossy optical channels per sent photon due to the two polarizations, but this assumes that the photon would have a single frequency contradicting the spatial localization of the photon pulse. However, if I assume a localized photon pulse, then the photon does not have a defined frequency anymore, but has a specific linewidth. Therefore, I would possibly use an uncountable number of frequencies and therefore also channels.

Have I misunderstood anything or is this bound not useful in realistic implementations of QKD?


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