216 research outputs found
Quantum Multi-Prover Interactive Proof Systems with Limited Prior Entanglement
This paper gives the first formal treatment of a quantum analogue of
multi-prover interactive proof systems. It is proved that the class of
languages having quantum multi-prover interactive proof systems is necessarily
contained in NEXP, under the assumption that provers are allowed to share at
most polynomially many prior-entangled qubits. This implies that, in
particular, if provers do not share any prior entanglement with each other, the
class of languages having quantum multi-prover interactive proof systems is
equal to NEXP. Related to these, it is shown that, in the case a prover does
not have his private qubits, the class of languages having quantum
single-prover interactive proof systems is also equal to NEXP.Comment: LaTeX2e, 19 pages, 2 figures, title changed, some of the sections are
fully revised, journal version in Journal of Computer and System Science
On the power of quantum, one round, two prover interactive proof systems
We analyze quantum two prover one round interactive proof systems, in which
noninteracting provers can share unlimited entanglement. The maximum acceptance
probability is characterized as a superoperator norm. We get some partial
results about the superoperator norm, and in particular we analyze the "rank
one" case.Comment: 12 pages, no figure
Quantum Proofs
Quantum information and computation provide a fascinating twist on the notion
of proofs in computational complexity theory. For instance, one may consider a
quantum computational analogue of the complexity class \class{NP}, known as
QMA, in which a quantum state plays the role of a proof (also called a
certificate or witness), and is checked by a polynomial-time quantum
computation. For some problems, the fact that a quantum proof state could be a
superposition over exponentially many classical states appears to offer
computational advantages over classical proof strings. In the interactive proof
system setting, one may consider a verifier and one or more provers that
exchange and process quantum information rather than classical information
during an interaction for a given input string, giving rise to quantum
complexity classes such as QIP, QSZK, and QMIP* that represent natural quantum
analogues of IP, SZK, and MIP. While quantum interactive proof systems inherit
some properties from their classical counterparts, they also possess distinct
and uniquely quantum features that lead to an interesting landscape of
complexity classes based on variants of this model.
In this survey we provide an overview of many of the known results concerning
quantum proofs, computational models based on this concept, and properties of
the complexity classes they define. In particular, we discuss non-interactive
proofs and the complexity class QMA, single-prover quantum interactive proof
systems and the complexity class QIP, statistical zero-knowledge quantum
interactive proof systems and the complexity class \class{QSZK}, and
multiprover interactive proof systems and the complexity classes QMIP, QMIP*,
and MIP*.Comment: Survey published by NOW publisher
Entanglement-Resistant Two-Prover Interactive Proof Systems and Non-Adaptive Private Information Retrieval Systems
We show that, for any language in NP, there is an entanglement-resistant
constant-bit two-prover interactive proof system with a constant completeness
vs. soundness gap. The previously proposed classical two-prover constant-bit
interactive proof systems are known not to be entanglement-resistant. This is
currently the strongest expressive power of any known constant-bit answer
multi-prover interactive proof system that achieves a constant gap. Our result
is based on an "oracularizing" property of certain private information
retrieval systems, which may be of independent interest.Comment: 8 page
Quantum interactive proofs and the complexity of separability testing
We identify a formal connection between physical problems related to the
detection of separable (unentangled) quantum states and complexity classes in
theoretical computer science. In particular, we show that to nearly every
quantum interactive proof complexity class (including BQP, QMA, QMA(2), and
QSZK), there corresponds a natural separability testing problem that is
complete for that class. Of particular interest is the fact that the problem of
determining whether an isometry can be made to produce a separable state is
either QMA-complete or QMA(2)-complete, depending upon whether the distance
between quantum states is measured by the one-way LOCC norm or the trace norm.
We obtain strong hardness results by proving that for each n-qubit maximally
entangled state there exists a fixed one-way LOCC measurement that
distinguishes it from any separable state with error probability that decays
exponentially in n.Comment: v2: 43 pages, 5 figures, completely rewritten and in Theory of
Computing (ToC) journal forma
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