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The concept of asymptotic correctability of Bell-diagonal quantum states isgeneralised to elementary quantum systems of higher dimensions. Based on theseresults basic properties of quantum state purification protocols areinvestigated which are capable of purifying tensor products of Bell-diagonalstates and which are based on $B$-steps of the Gottesman-Lo-type with thesubsequent application of a Calderbank-Shor-Steane quantum code. Consequencesfor maximum tolerable error rates of quantum cryptographic protocols arediscussed.Comment: submitted to J. Phys.

Asymptotic correctability of Bell-diagonal qudit states and lower bounds on tolerable error probabilities in quantum cryptography