Determining the worst-case uncertainty added by a quantum circuit is shown to be computationally intractable. This is the problem of detecting when a quantum channel implemented as a circuit is close to a linear isometry, and it is shown to be complete for the complexity class QMA of verifiable quantum computation. The main idea is to relate the problem of detecting when a channel is close to an isometry to the problem of determining how mixed the output of the channel can be when the input is a pure state.


Pure State Quantum Channel Input State Quantum Circuit Physical Review Letter 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Bill Rosgen
    • 1
  1. 1.Centre for Quantum TechnologiesNational University of SingaporeSingapore

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