Some bounds on the minimum number of queries required for quantum channel perfect discrimination

We prove a lower bound on the q-maximal fidelities between two quantum channels ε 0 and ε 1 and an upper bound on the q-maximal fidelities between a quantum channel ε and an identity I. Then we apply these two bounds to provide a simple sufficient and necessary condition for sequential perfect distinguish ability between ε and I and provide both a lower bound and an upper bound on the minimum number of queries required to sequentially perfectly discriminating ε and I. Interestingly, in the 2-dimensional case, both bounds coincide. Based on the optimal perfect discrimination protocol presented in [20], we can further generalize the lower bound and upper bound to the minimum number of queries to perfectly discriminating ε and I over all possible discrimination schemes. Finally the two lower bounds are shown remain working for perfectly discriminating general two quantum channels ε 0 and ε 1 in sequential scheme and over all possible discrimination schemes respectively. © Rinton Press