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Theory Seminar: Quantum Multi Prover Interactive Proofs with Communicating Provers
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Avinatan Hassidim, (Hebrew University of Jerusalem)
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Sunday, 22.6.2008, 11:00
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Room 337-8 Taub Bld.
We introduce a variant of Quantum Multi Prover Interactive Proofs (QMIP), where the provers do not share entanglement, the communication between the verifier and the provers is quantum, but the provers are unlimited in the classical communication between them. At first, this model may seem very weak, as provers who exchange information seem to be equivalent in power to a simple prover. This in fact is not the case - we show that any language in NEXP can be recognized in this model efficiently, with just two provers and two rounds of communication, with a constant completeness-soundness gap.

The main idea is not to bound the information the provers exchange with each other, as in the classical case, but rather to prove that any ``cheating'' strategy employed by the provers has constant probability to diminish the entanglement between the verifier and the provers by a constant amount. Detecting such reduction gives us the soundness proof. Similar ideas and techniques may help help with other models of Quantum MIP, including the dual question, of non communicating provers with unlimited entanglement.

Joint work with Michael Ben-Or and Haran Pilpel
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