  The dimension reduction method enables security proofs of quantum key
distribution (QKD) protocols that are originally formulated in infinite
dimensions via reduction to a tractable finite-dimensional optimization. The
reduction of dimensions is associated with a correction term in the secret key
rate calculation. The previously derived correction term is loose when the
protocol measurements are nearly block-diagonal with respect to the projection
onto the reduced finite-dimensional subspace. Here, we provide a tighter
correction term. It interpolates between the two extreme cases where all
measurement operators are block-diagonal, and where at least one has maximally
large off-diagonal blocks. This new correction term can reduce the
computational overhead of applying the dimension reduction method by reducing
the required dimension of the chosen subspace.
