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24
Quantum ArthurMerlin games
 Computational Complexity
"... Abstract This paper studies quantum ArthurMerlin games, whichare a restricted form of quantum interactive proof system in which the verifier's messages are given by unbiased coinflips. The following results are proved. ffl For onemessage quantum ArthurMerlin games, whichcorrespond to the co ..."
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Cited by 71 (4 self)
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Abstract This paper studies quantum ArthurMerlin games, whichare a restricted form of quantum interactive proof system in which the verifier's messages are given by unbiased coinflips. The following results are proved. ffl For onemessage quantum ArthurMerlin games, whichcorrespond to the complexity class QMA, completeness and soundness errors can be reduced exponentially without increasing the length of Merlin's message. Previous constructions for reducing error required a polynomial increase in the length of Merlin's message. Applications of this fact include a proof that logarithmic length quantum certificates yield no increase in powerover BQP and a simple proof that QMA ` PP. ffl In the case of three or more messages, quantum ArthurMerlin games are equivalent in power to ordinary quantum interactive proof systems. In fact, for any languagehaving a quantum interactive proof system there exists a threemessage quantum ArthurMerlin game in whichArthur's only message consists of just a single coinflip that achieves perfect completeness and soundness errorexponentially close to 1/2. ffl Any language having a twomessage quantum ArthurMerlin game is contained in BP \Delta PP. This gives somesuggestion that three messages are stronger than two in
Quantum interactive proofs with competing provers
 In Proceedings of the 22nd Symposium on Theoretical Aspects of Computer Science (2005
"... This paper studies quantum refereed games, which are quantum interactive proof systems with two competing provers: one that tries to convince the verifier to accept and the other that tries to convince the verifier to reject. We prove that every language having an ordinary quantum interactive proof ..."
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Cited by 20 (11 self)
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This paper studies quantum refereed games, which are quantum interactive proof systems with two competing provers: one that tries to convince the verifier to accept and the other that tries to convince the verifier to reject. We prove that every language having an ordinary quantum interactive proof system also has a quantum refereed game in which the verifier exchanges just one round of messages with each prover. A key part of our proof is the fact that there exists a single quantum measurement that reliably distinguishes between mixed states chosen arbitrarily from disjoint convex sets having large minimal trace distance from one another. We also show how to reduce the probability of error for some classes of quantum refereed games. 1
Semidefinite programs for completely bounded norms
, 2009
"... The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate proofs of some known facts about them. ..."
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Cited by 20 (3 self)
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The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate proofs of some known facts about them.
www.stacsconf.org DISTINGUISHING SHORT QUANTUM COMPUTATIONS
"... Abstract. Distinguishing logarithmic depth quantum circuits on mixed states is shown to be complete for QIP, the class of problems having quantum interactive proof systems. Circuits in this model can represent arbitrary quantum processes, and thus this result has implications for the verification of ..."
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Abstract. Distinguishing logarithmic depth quantum circuits on mixed states is shown to be complete for QIP, the class of problems having quantum interactive proof systems. Circuits in this model can represent arbitrary quantum processes, and thus this result has implications for the verification of implementations of quantum algorithms. The distinguishability problem is also complete for QIP on constant depth circuits containing the unbounded fanout gate. These results are shown by reducing a QIPcomplete problem to a logarithmic depth version of itself using a parallelization technique. 1.
General properties of quantum zeroknowledge proofs
 In Proceedings of the Fifth IACR Theory of Cryptography Conference
, 2008
"... This paper studies the complexity classes QZK and HVQZK, the classes of problems having a quantum computational zeroknowledge proof system and an honestverifier quantum computational zeroknowledge proof system, respectively. The results proved in this paper include: • HVQZK = QZK. • Any problem i ..."
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This paper studies the complexity classes QZK and HVQZK, the classes of problems having a quantum computational zeroknowledge proof system and an honestverifier quantum computational zeroknowledge proof system, respectively. The results proved in this paper include: • HVQZK = QZK. • Any problem in QZK has a publiccoin quantum computational zeroknowledge proof system. • Any problem in QZK has a quantum computational zeroknowledge proof system of perfect completeness. • Any problem in QZK has a threemessage publiccoin quantum computational zeroknowledge proof system of perfect completeness with polynomially small error in soundness (hence with arbitrarily small constant error in soundness). All the results proved in this paper are unconditional, i.e., they do not rely any computational assumptions such as the existence of quantum oneway functions or permutations. For the classes QPZK, HVQPZK, and QSZK of problems having a quantum perfect zeroknowledge proof system, an honestverifier quantum perfect zeroknowledge proof system, and a quantum statistical zeroknowledge proof system, respectively, the following new properties are proved:
NonIdentity Check Remains QMAComplete for Short Circuits
, 2008
"... The NonIdentity Check problem asks whether a given a quantum circuit is far away from the identity or not. It is well known that this problem is QMAComplete [14]. In this note, it is shown that the NonIdentity Check problem remains QMAComplete for circuits of short depth. Specifically, we prove ..."
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The NonIdentity Check problem asks whether a given a quantum circuit is far away from the identity or not. It is well known that this problem is QMAComplete [14]. In this note, it is shown that the NonIdentity Check problem remains QMAComplete for circuits of short depth. Specifically, we prove that for constant depth quantum circuit in which each gate is given to at least Ω(log n) bits of precision, the NonIdentity Check problem is QMAComplete. It also follows that the hardness of the problem remains for polylogarithmic depth circuit consisting of only gates from any universal gate set and for logarithmic depth circuit using some specific universal gate set. 1