# zbMATH — the first resource for mathematics

Some bounds on the minimum number of queries required for quantum channel perfect discrimination. (English) Zbl 1268.81037
Summary: We prove a lower bound on the $$q$$-maximal fidelities between two quantum channels $$\mathcal{E}_0$$ and $$\mathcal{E}_1$$ and an upper bound on the $$q$$-maximal fidelities between a quantum channel $$\mathcal{E}$$ and an identity $$\mathcal{I}$$. Then we apply these two bounds to provide a simple sufficient and necessary condition for sequential perfect distinguishability between $$\mathcal{E}$$ and $$\mathcal{I}$$ and provide both a lower bound and an upper bound on the minimum number of queries required to sequentially perfectly discriminating $$\mathcal{E}$$ and $$\mathcal{I}$$. Interestingly, in the 2-dimensional case, both bounds coincide. Based on the optimal perfect discrimination protocol presented in [R. Y. Duan, Y. Feng, and M. S. Ying, “Perfect distinguishability of quantom operations”, in: Phys. Rev. Lett. 103, No. 21, Article ID 210501, 4 p. (2009)], we can further generalize the lower bound and upper bound to the minimum number of queries to perfectly discriminating $$\mathcal{E}$$ and $$\mathcal{I}$$ over all possible discrimination schemes. Finally the two lower bounds are shown remain working for perfectly discriminating general two quantum channels $$\mathcal{E}_0$$ and $$\mathcal{E}_1$$ in sequential scheme and over all possible discrimination schemes respectively.

##### MSC:
 81P45 Quantum information, communication, networks (quantum-theoretic aspects) 94A40 Channel models (including quantum) in information and communication theory