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Quantum multiprover interactive proof systems with limited prior entanglement
 Journal of Computer and System Sciences
"... This paper gives the first formal treatment of a quantum analogue of multiprover interactive proof systems. In quantum multiprover interactive proof systems there can be two natural situations: one is with prior entanglement among provers, and the other does not allow prior entanglement among prov ..."
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This paper gives the first formal treatment of a quantum analogue of multiprover interactive proof systems. In quantum multiprover interactive proof systems there can be two natural situations: one is with prior entanglement among provers, and the other does not allow prior entanglement among provers. This paper focuses on the latter situation and proves that, if provers do not share any prior entanglement each other, the class of languages that have quantum multiprover interactive proof systems is equal to NEXP. It implies that the quantum multiprover interactive proof systems without prior entanglement have no gain to the classical ones. This result can be extended to the following statement of the cases with prior entanglement: if a language L has a quantum multiprover interactive proof system allowing at most polynomially many prior entangled qubits among provers, L is necessarily in NEXP. Another interesting result shown in this paper is that, in the case the prover does not have his private qubits, the class of languages that have singleprover quantum interactive proof systems is also equal to NEXP. Our results are also of importance in the sense of giving exact correspondances between quantum and classical complexity classes, because there have been known only a few results giving such correspondances.
Uniform Generation of NPwitnesses using an NPoracle
 Information and Computation
, 1997
"... A Uniform Generation procedure for NP is an algorithm which given any input in a fixed NPlanguage, outputs a uniformly distributed NPwitness for membership of the input in the language. We present a Uniform Generation procedure for NP that runs in probabilistic polynomialtime with an NPoracle. T ..."
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A Uniform Generation procedure for NP is an algorithm which given any input in a fixed NPlanguage, outputs a uniformly distributed NPwitness for membership of the input in the language. We present a Uniform Generation procedure for NP that runs in probabilistic polynomialtime with an NPoracle. This improves upon results of Jerrum, Valiant and Vazirani, which either require a \Sigma P 2 oracle or obtain only almost uniform generation. Our procedure utilizes ideas originating in the works of Sipser, Stockmeyer, and Jerrum, Valiant and Vazirani. Dept. of Computer Science & Engineering, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA. EMail: mihir@cs.ucsd.edu. URL: http://wwwcse.ucsd.edu/users/mihir. Supported in part by NSF CAREER Award CCR9624439 and a 1996 Packard Foundation Fellowship in Science and Engineering. y Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel. EMail: oded@wis...
Error Reduction By Parallel Repetition  the State of the Art
, 1995
"... We show that no fixed number of parallel repetitions suffices in order to reduce the error in twoprover oneround proof systems from one constant to another. Our results imply that the recent bounds proven by Ran Raz, showing that the number of rounds that suffice is inversely proportional to the a ..."
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We show that no fixed number of parallel repetitions suffices in order to reduce the error in twoprover oneround proof systems from one constant to another. Our results imply that the recent bounds proven by Ran Raz, showing that the number of rounds that suffice is inversely proportional to the answer length, are nearly best possible. Our proof technique builds upon an idea of Oleg Verbitsky. We use this opportunity to survey the known results on parallel repetition, and to present the proofs of some previously claimed theorems. 1 Introduction A two prover one round proof system [8], MIP(2,1), is a protocol by which two provers jointly try to convince a computationally limited probabilistic verifier that a common input belongs to a prespecified language. The verifier selects a pair of questions at random. Each prover sees only one of the two questions, and sends back an answer. The verifier evaluates a predicate on the common input and the two questions and answers, and accepts or ...