22 research outputs found
Quantum Interactive Proofs with Competing Provers
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.Comment: 13 pages, to appear in STACS 200
Toward a general theory of quantum games
We study properties of quantum strategies, which are complete specifications
of a given party's actions in any multiple-round interaction involving the
exchange of quantum information with one or more other parties. In particular,
we focus on a representation of quantum strategies that generalizes the
Choi-Jamio{\l}kowski representation of quantum operations. This new
representation associates with each strategy a positive semidefinite operator
acting only on the tensor product of its input and output spaces. Various facts
about such representations are established, and two applications are discussed:
the first is a new and conceptually simple proof of Kitaev's lower bound for
strong coin-flipping, and the second is a proof of the exact characterization
QRG = EXP of the class of problems having quantum refereed games.Comment: 23 pages, 12pt font, single-column compilation of STOC 2007 final
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Parallel approximation of non-interactive zero-sum quantum games
This paper studies a simple class of zero-sum games played by two competing
quantum players: each player sends a mixed quantum state to a referee, who
performs a joint measurement on the two states to determine the players'
payoffs. We prove that an equilibrium point of any such game can be
approximated by means of an efficient parallel algorithm, which implies that
one-turn quantum refereed games, wherein the referee is specified by a quantum
circuit, can be simulated in polynomial space.Comment: 18 page
Dequantizing read-once quantum formulas
Quantum formulas, defined by Yao [FOCS '93], are the quantum analogs of
classical formulas, i.e., classical circuits in which all gates have fanout
one. We show that any read-once quantum formula over a gate set that contains
all single-qubit gates is equivalent to a read-once classical formula of the
same size and depth over an analogous classical gate set. For example, any
read-once quantum formula over Toffoli and single-qubit gates is equivalent to
a read-once classical formula over Toffoli and NOT gates. We then show that the
equivalence does not hold if the read-once restriction is removed. To show the
power of quantum formulas without the read-once restriction, we define a new
model of computation called the one-qubit model and show that it can compute
all boolean functions. This model may also be of independent interest.Comment: 14 pages, 8 figures, to appear in proceedings of TQC 201
Quantum Arthur-Merlin Games
This paper studies quantum Arthur-Merlin games, which are Arthur-Merlin games
in which Arthur and Merlin can perform quantum computations and Merlin can send
Arthur quantum information. As in the classical case, messages from Arthur to
Merlin are restricted to be strings of uniformly generated random bits. It is
proved that for one-message quantum Arthur-Merlin games, which correspond 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 power over BQP and a simple
proof that QMA is contained in PP. Other facts that are proved include the
equivalence of three (or more) message quantum Arthur-Merlin games with
ordinary quantum interactive proof systems and some basic properties concerning
two-message quantum Arthur-Merlin games.Comment: 22 page