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A method to quantify the error probability at the Kirchhoff-law-Johnson-noise (KLJN) secure key exchange is introduced. The types of errors due to statistical inaccuracies in noise voltage measurements are classified and the error probability is calculated. The most interesting finding is that the error probability decays exponentially with the duration of the time window of single bit exchange. The results indicate that it is feasible to have so small error probabilities of the exchanged bitsdoi:10.1371/journal.pone.0081103 pmid:24303033 pmcid:PMC3841199 fatcat:4u5v5rhtkna7pcwgu7zb7r67im