  Due to the capability of tolerating high error rate and generating more key
bits per trial, high-dimensional quantum key distribution attracts wide
interest. Despite great progresses in high-dimensional quantum key
distribution, there are still some gaps between theory and experiment. One of
these is that the security of the secret key heavily depends on the number of
the emitted signals. So far, the existing security proofs are only suitable in
the case with an infinite or unpractically large number of emitted signals.
Here, by introducing the idea of "key classification" and developing relevant
techniques based on the uncertainty relation for smooth entropies, we propose a
tight finite-key analysis suitable for generalized high-dimensional quantum key
distribution protocols. Benefitting from our theory, high-dimensional quantum
key distribution protocols with finite resources become experimentally
feasible.
