  We calculate an achievable secret key rate for quantum key distribution with
a finite number of signals, by evaluating the min-entropy explicitly. The
min-entropy can be expressed in terms of the guessing probability, which we
calculate for d-dimensional systems. We compare these key rates to previous
approaches using the von Neumann entropy and find non-zero key rates for a
smaller number of signals. Furthermore, we improve the secret key rates by
modifying the parameter estimation step. Both improvements taken together lead
to non-zero key rates for only 10^4-10^5 signals. An interesting conclusion can
also be drawn from the additivity of the min-entropy and its relation to the
guessing probability: for a set of symmetric tensor product states the optimal
minimum-error discrimination (MED) measurement is the optimal MED measurement
on each subsystem.
