Optimal sequential state discrimination between two mixed quantum states

Recently, sequential state discrimination, as a quantum-key distribution protocol, has been proposed for multiple receivers. A previous study [J. A. Bergou et al., Phys. Rev. Lett. 111, 100501 (2013)] showed that every receiver could successfully perform a sequential state discrimination of two pure states with identical prior probabilities. In this study, we extend the sequential state discrimination to mixed states with arbitrary prior probability. First, we analytically obtain the condition of the receiver's optimal measurement. In addition, we show that the optimal probability for every receiver to share the mixed state prepared by the sender is not zero. Furthermore, we compare the sequential state discrimination to the strategies of quantum reproducing and quantum broadcasting. We find that there are cases in which, unlike that of the pure state, the sequential state discrimination of mixed states shows a better performance than the other strategies.We thank Donghoon Ha and Jihwan Kim for their insightful discussions. This work is supported by the Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF2015R1D1A1A01060795) and Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (MSIP) (No. R0190-15-2028, PSQKD)