  The concept of asymptotic correctability of Bell-diagonal quantum states is
generalised to elementary quantum systems of higher dimensions. Based on these
results basic properties of quantum state purification protocols are
investigated which are capable of purifying tensor products of Bell-diagonal
states and which are based on $B$-steps of the Gottesman-Lo-type with the
subsequent application of a Calderbank-Shor-Steane quantum code. Consequences
for maximum tolerable error rates of quantum cryptographic protocols are
discussed.
