37 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
Non-Locality in Interactive Proofs
In multi-prover interactive proofs (MIPs), the verifier is usually
non-adaptive. This stems from an implicit problem which we call
``contamination'' by the verifier. We make explicit the verifier contamination
problem, and identify a solution by constructing a generalization of the MIP
model. This new model quantifies non-locality as a new dimension in the
characterization of MIPs. A new property of zero-knowledge emerges naturally as
a result by also quantifying the non-locality of the simulator.Comment: 32 pages, 14 figures. Submitted to Crypto 2019, Feb 2019. Report
arXiv:1804.02724 merged here in the update proces
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
Efficient holographic proofs
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.Includes bibliographical references (p. 57-63).by Alexander Craig Russell.Ph.D
Contamination in Cryptographic Protocols
We discuss a foundational issue in multi-prover interactive proofs (MIP) which we call "contamination" by the verifier. We propose a model which accounts for, and controls, verifier contamination, and show that this model does not lose expressive power. A new characterization of zero-knowledge naturally follows. We show the usefulness of this model by constructing a practical MIP for NP where the provers are spatially separated. Finally, we relate our model to the practical problem of e-voting by constructing a functional voter roster based on distributed trust
Preuves interactives quantiques
Cette thèse est consacrée à la complexité basée sur le paradigme des preuves interactives.
Les classes ainsi définies ont toutes en commun qu’un ou plusieurs prouveurs,
infiniment puissants, tentent de convaincre un vérificateur, de puissance bornée, de
l’appartenance d’un mot à un langage. Nous abordons ici le modèle classique, où les
participants sont des machines de Turing, et le modèle quantique, où ceux-ci sont
des circuits quantiques. La revue de littérature que comprend cette thèse s’adresse
à un lecteur déjà familier avec la complexité et l’informatique quantique.
Cette thèse présente comme résultat la caractérisation de la classe NP par une
classe de preuves interactives quantiques de taille logarithmique.
Les différentes classes sont présentées dans un ordre permettant d’aborder aussi
facilement que possible les classes interactives. Le premier chapitre est consacré aux
classes de base de la complexité ; celles-ci seront utiles pour situer les classes subséquemment
présentées. Les chapitres deux et trois présentent respectivement les
classes à un et à plusieurs prouveurs. La présentation du résultat ci-haut mentionné
est l’objet du chapitre quatre.This thesis is devoted to complexity theory based on the interactive proof paradigm.
All classes defined in this way involve one or many infinitely powerful provers
attempting to convince a verifier of limited power that a string belongs to a certain
language. We will consider the classical model, in which the various participants
are Turing machines, as well as the quantum model, in which they are quantum
circuits. The literature review included in this thesis assume that the reader is
familiar with the basics of complexity theory and quantum computing.
This thesis presents the original result that the class NP can be characterized
by a class of quantum interactive proofs of logarithmic size.
The various classes are presented in an order that facilitates the treatment of
interactive classes. The first chapter is devoted to the basic complexity classes;
these will be useful points of comparison for classes presented subsequently. Chapters
two and three respectively present classes with one and many provers. The
presentation of the result mentioned above is the object of chapter four