computational complexity

, Volume 17, Issue 2, pp 282–299

Perfect Parallel Repetition Theorem for Quantum Xor Proof Systems

  • Richard Cleve
  • William Slofstra
  • Falk Unger
  • Sarvagya Upadhyay
Article

Abstract.

We consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier’s verdict is a function of the XOR of the two bits received. We show that, when the provers are allowed to coordinate their behavior using a shared entangled quantum state, a perfect parallel repetition theorem holds in the following sense. The prover’s optimal success probability for simultaneously playing a collection of XOR proof systems is exactly the product of the individual optimal success probabilities. This property is remarkable in view of the fact that, in the classical case (where the provers can only utilize classical information), it does not hold. The theorem is proved by analyzing parities of XOR proof systems using semidefinite programming techniques, which we then relate to parallel repetitions of XOR games via Fourier analysis.

Keywords.

Quantum computing interactive proof systems parallel repetition 

Subject classification.

81P68 68Q10 

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Copyright information

© Birkhaeuser 2008

Authors and Affiliations

  • Richard Cleve
    • 1
    • 2
  • William Slofstra
    • 3
  • Falk Unger
    • 4
  • Sarvagya Upadhyay
    • 5
  1. 1.School of Computer Science and Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  3. 3.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA
  4. 4.CWIAmsterdamThe Netherlands
  5. 5.School of Computer Science and Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada

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