Quantum Two Proves Interactive Proof Systems
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Quantum Two Proves Interactive Proof Systems
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Author : Alex Rapaport
language : en
Publisher:
Release Date : 2007
Quantum Two Proves Interactive Proof Systems written by Alex Rapaport and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Quantum computers categories.
Quantum Interactive Proofs And The Complexity Of Entanglement Detection
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Author : Kevin Milner
language : en
Publisher:
Release Date : 2014
Quantum Interactive Proofs And The Complexity Of Entanglement Detection written by Kevin Milner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
"This thesis identifies a formal connection between physical problems related to entanglement detection and complexity classes in theoretical computer science. In particular, we prove that to nearly every quantum interactive proof complexity class (including BQP, QMA, QMA(2), QSZK, and QIP), there corresponds a natural entanglement or correlation detection problem that is complete for that class. In this sense, we can say that an entanglement or correlation detection problem captures the expressive power of each quantum interactive proof complexity class, and the contrast between such problems gives intuition to the differences between classes of quantum interactive proofs. It is shown that the difficulty of entanglement detection also depends on whether the distance measure used is the trace distance or the one-way LOCC distance. We also provide analysis for another problem of this flavour, which we show is decidable by a two-message quantum interactive proof system while being hard for both NP and QSZK, the first nontrivial example of such a problem." --
Quantum Proofs
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Author : Thomas Vidick
language : en
Publisher: Foundations and Trends (R) in Theoretical Computer Science
Release Date : 2016-03-30
Quantum Proofs written by Thomas Vidick and has been published by Foundations and Trends (R) in Theoretical Computer Science this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-30 with categories.
Quantum Proofs provides 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, it discusses 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 QSZK, and multiprover interactive proof systems and the complexity classes QMIP, QMIP*, and MIP*. Quantum Proofs is mainly intended for non-specialists having a basic background in complexity theory and quantum information. A typical reader may be a student or researcher in either area desiring to learn about the fundamentals of the (actively developing) theory of quantum interactive proofs.
Introduction To Quantum Interactive Proof Systems
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Author : Shahab Razavi
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2010-06
Introduction To Quantum Interactive Proof Systems written by Shahab Razavi and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06 with categories.
Over the last few decades, the limitations of classical computing demand for a new way of computation. One such limit can be found in classical interactive proof systems. Quantum computing sounds promising enough in overcoming those limits. Although there are many great books on this subject, a short introduction to quantum interactive proof systems which gives the reader an intuition of the subject was lacking. This book, therefore, provides such an intuition by firstly introducing the basic concepts and secondly by defining some of the quantum computational classes based on their classical counterparts. At the end a quantum oracle separation of QMA and QCMA is presented which helps the reader in better understanding of differences between quantum and classical interactive proof systems.
Quantum Information And Variants Of Interactive Proof Systems
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Author : Sarvagya Upadhyay
language : en
Publisher:
Release Date : 2011
Quantum Information And Variants Of Interactive Proof Systems written by Sarvagya Upadhyay and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
For nearly three decades, the model of interactive proof systems and its variants have been central to many important and exciting developments in computational complexity theory such as exact characterization of some well known complexity classes, development of probabilistically checkable proof systems and theory of hardness of approximation, and formalization of fundamental cryptographic primitives. On the other hand, the theory of quantum information, which is primarily concerned with harnessing quantum mechanical features for algorithmic, cryptographic, and information processing tasks has found many applications. In the past three decades, quantum information has been used to develop unconditionally secure quantum cryptography protocols, efficient quantum algorithms for certain problems that are believed to be intractable in classical world, and communication efficient protocols. In this thesis, we study the impact of quantum information on the models of interactive proof systems and their multi-prover variants. We study various quantum models and explore two questions. The first question we address pertains to the expressive power of such models with or without resource constraints. The second question is related to error reduction technique of such proof systems via parallel repetition.
Entangled Protocols And Non Local Games For Testing Quantum Systems
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Author : Matthew Ryan Coudron.
language : en
Publisher:
Release Date : 2017
Entangled Protocols And Non Local Games For Testing Quantum Systems written by Matthew Ryan Coudron. and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
The field of quantum computing investigates the extent to which one can design a quantum system that outperforms all known classical hardware at a certain task. But, to what extent can a human being, capable only (perhaps) of classical computation and of observing classical bit-string messages, verify that a quantum device in their possession is performing the task that they wish? This is a fundamental question about the nature of quantum mechanics, and the extent to which humans can harness it in a trustworthy manner. It is also a natural and important consideration when quantum devices may be used to perform sensitive cryptographic tasks which have no known efficient classical witness of correctness (Quantum Key Distribution, and Randomness Expansion are two examples of such tasks). It is remarkable that any quantum behavior at all can be tested by a verifier under such a constraint, without trusting any other quantum mechanical device in the process! But, intriguingly, when there are two or more quantum provers available in an interactive proof, there exist protocols to verify many interesting and useful quantum tasks in this setting. This thesis investigates multi-prover interactive proofs for verifying quantum behavior, and focuses on the stringent testing scenario in which the verifier in the interactive proof is completely classical as described above. It resolves the question of the maximum attainable expansion rate of a randomness expansion protocol by providing an adaptive randomness expansion protocol that achieves an arbitrary, or infinite rate of randomness expansion [29]. Secondly it presents a new rigidity result for the parallel repeated magic square game [24], which provides some improvements on previous rigidity results that play a pivotal role in existing interactive proofs for entangled provers, QKD, and randomness expansion results. This new rigidity result may be useful for improving such interactive proofs in the future. The second half of this thesis investigates the problem of bounding the role of quantum entanglement in non-local processes. This is important for understanding the upper limit on the power of multi-prover interactive proof systems with entangled provers. In particular it establishes that, assuming the Strong Kirchberg Conjecture, one can provide a doubly exponential upper bound on the class MIP* [25] (for comparison, the best known unconditional upper bound on MIP* is that its languages are recursively enumerable!). Finally this thesis presents a result which characterizes the type of entanglement that is useful in entanglement assisted quantum communication complexity by showing that any communication protocol using arbitrary shared entanglement can be simulated by a protocol using only EPR pairs for shared entanglement. Therefore all quantum communication protocols can be approximately simulated by a protocol using only the maximally entangled state as a shared resource.
Quantum Two Proverbs Interactive Proof Sistems
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Author : Alex Rapaport
language : en
Publisher:
Release Date : 2007
Quantum Two Proverbs Interactive Proof Sistems written by Alex Rapaport and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Algorithms And Computation
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Author : Prosenjit K. Bose
language : en
Publisher: Springer
Release Date : 2003-08-02
Algorithms And Computation written by Prosenjit K. Bose and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-02 with Mathematics categories.
Annotation. This book constitutes the refereed proceedings of the 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002, held in Vancouver, BC, Canada in November 2002. The 54 revised full papers presented together with 3 invited contributions were carefully reviewed and selected from close to 160 submissions. The papers cover all relevant topics in algorithmics and computation, in particular computational geometry, algorithms and data structures, approximation algorithms, randomized algorithms, graph drawing and graph algorithms, combinatorial optimization, computational biology, computational finance, cryptography, and parallel and distributedd algorithms.
Quantum Computation
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Author : American Mathematical Society. Short Course
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Quantum Computation written by American Mathematical Society. Short Course and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Computers categories.
This book presents written versions of the eight lectures given during the AMS Short Course held at the Joint Mathematics Meetings in Washington, D.C. The objective of this course was to share with the scientific community the many exciting mathematical challenges arising from the new field of quantum computation and quantum information science. The course was geared toward demonstrating the great breadth and depth of this mathematically rich research field. Interrelationships withexisting mathematical research areas were emphasized as much as possible. Moreover, the course was designed so that participants with little background in quantum mechanics would, upon completion, be prepared to begin reading the research literature on quantum computation and quantum informationscience. Based on audience feedback and questions, the written versions of the lectures have been greatly expanded, and supplementary material has been added. The book features an overview of relevant parts of quantum mechanics with an introduction to quantum computation, including many potential quantum mechanical computing devices; introduction to quantum algorithms and quantum complexity theory; in-depth discussion on quantum error correcting codes and quantum cryptography; and finally,exploration into diverse connections between quantum computation and various areas of mathematics and physics.
Algorithms And Computation
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Author : Prosenjit Bose
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-11-08
Algorithms And Computation written by Prosenjit Bose and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-11-08 with Mathematics categories.
This book constitutes the refereed proceedings of the 13th Annual International Symposium on Algorithms and Computation, ISAAC 2002, held in Vancouver, BC, Canada in November 2002. The 54 revised full papers presented together with 3 invited contributions were carefully reviewed and selected from close to 160 submissions. The papers cover all relevant topics in algorithmics and computation, in particular computational geometry, algorithms and data structures, approximation algorithms, randomized algorithms, graph drawing and graph algorithms, combinatorial optimization, computational biology, computational finance, cryptography, and parallel and distributedd algorithms.