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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
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