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### Volume 2013

#### Article 11

Published by the Department of Computer Science, The University of Chicago.

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Coherent state exchange in multi-prover quantum
interactive proof systems

Debbie Leung

Department of Combinatorics and Optimization

University of Waterloo

Waterloo, Ont., Canada

`wcleung AT uwaterloo DOT ca `

Ben Toner

School of Physics

University of Melbourne

`bentoner AT bentoner DOT com`

and

John Watrous

School of Computer Science

University of Waterloo

`john DOT watrous AT uwaterloo DOT ca`

*August 13, 2013*
#### Abstract

We show that any number of parties can coherently exchange any one
pure quantum state for another, without communication, given prior
shared entanglement.
Two applications of this fact to the study of multi-prover quantum
interactive proof systems are given.
First, we prove that there exists a one-round two-prover quantum
interactive proof system for which no finite amount of shared
entanglement allows the provers to implement an optimal strategy.
More specifically, for every fixed input string, there exists a
sequence of strategies for the provers, with each strategy requiring
more entanglement than the last, for which the probability for the
provers to convince the verifier to accept approaches one.
It is not possible, however, for the provers to convince the
verifier to accept with certainty with a finite amount of shared
entanglement.
The second application is a simple proof that multi-prover quantum
interactive proofs can be transformed to have near-perfect
completeness by the addition of one round of communication.

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Submitted December 17, 2012, revised August 9, 2013; published August 13, 2013.

Article 10
Article 12

Volume 2013
Published articles