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

  • Authors:

  • Cheng Lu;Jianxin Chen;Runyao Duan

  • Affiliations:

  • Department of Computer Science and Technology, Tsinghua University, Beijing, China;Department of Computer Science and Technology, Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing, China;Centre for Quantum Computation and Intelligent Systems, University of Technology, Sydney, NSW, Australia

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2012

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Abstract

We prove a lower bound on the q-maximal fidelities between two quantum channels E0 and E1 and an upper bound on the q-maximal fidelities between a quantum channel E and an identity I. Then we apply these two bounds to provide a simple sufficient and necessary condition for sequential perfect distinguishability between E and I and provide both a lower bound and an upper bound on the minimum number of queries required to sequentially perfectly discriminating E 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 E and I over all possible discrimination schemes. Finally the two lower bounds are shown remain working for perfectly discriminating general two quantum channels E0 and E1 in sequential scheme and over all possible discrimination schemes respectively.