Analysis of the unambiguous state discrimination with unequal a priori probabilities

In this paper, we study unambiguous state discrimination regarding advanced attack on phase-coded quantum key distribution protocol. We propose the method of optimal unambiguous state discrimination probability derivation as a function of a priori probabilities for signal states. The expression obtained as an example in case of two signal states explicitly demonstrates the additional term dependent on small deviations from equal a priori probabilities that may take place in real quantum key distribution implementations. Precise estimation of optimal unambiguous state discrimination probability is significant for complete evaluation of quantum key distribution security.