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Springer eBooks

Quantum Information, Computation and Cryptography: An Introductory Survey of Theory, Technology and Experiments

Fabio Benatti, M. Fannes, Roberto Floreanini B, Dimitri Petritis

Published Sep 21, 2010• 13 citations
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Related papers

Quantum Information, Computation and Cryptography

Fabio Benatti, M. Fannes, Roberto Floreanini B +1 more

Lecture notes in physics•Jan 1, 2010•57 citations

Quantum random walks - an introductory overview

Julia Kempe, Albert Einstein

This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physical effects and computer science applications, introducing some of the main concepts and language of present day quantum information science in this context. We will mention recent developments in this new area and outline some open questions. 1. Overview Ever since the discovery of quantum mechanics people have been puzzled by the counter-intuitive character of the laws of nature. Over time we have learned to accept more and more effects that are unimaginable in a classical Newtonian world. Modern technology exploits quantum effects both to our benefit and detriment—among the memorable examples we should cite laser technology and not omit the atomic bomb. In recent years interest in quantum information theory has been generated by the prospect of employing its laws to design devices of surprising power [1]. New ideas include quantum cryptography [2, 3] and quantum computation. In 1994 Shor [4] discovered a quantum algorithm to factor numbers efficiently (that is in time that grows only polynomically with the length of the number to be factored). This has unleashed a wave of activity across a broad range of disciplines: physics, computer science, mathematics and engineering. This fruitful axis of research has uncovered many new effects that are strikingly different from their classical counterparts, both from the physical point of view as well as from a computer science and communication theory perspective. Over time these communities have gained a greater understanding of the concepts and notions of the other. The idea that information cannot be separated from

•Jan 1, 2003•920 citations

Quantum information science and its contributions to mathematics : American Mathematical Society Short Course, January 3-4, 2009, Washington, DC

Samuel J. Lomonaco

This volume is based on lectures delivered at the 2009 AMS Short Course on Quantum Computation and Quantum Information, held January 3-4, 2009, in Washington, D.C. Part I of this volume consists of two papers giving introductory surveys of many of the important topics in the newly emerging field of quantum computation and quantum information, i.e., quantum information science (QIS). The first paper discusses many of the fundamental concepts in QIS and ends with the curious and counter-intuitive phenomenon of entanglement concentration. The second gives an introductory survey of quantum error correction and fault tolerance, QIS's first line of defence against quantum decoherence. Part II consists of four papers illustrating how QIS research is currently contributing to the development of new research directions in mathematics. The first paper illustrates how differential geometry can be a fundamental research tool for the development of compilers for quantum computers. The second paper gives a survey of many of the connections between quantum topology and quantum computation. The last two papers give an overview of the new and emerging field of quantum knot theory, an interdisciplinary research field connecting quantum computation and knot theory. These two papers illustrate surprising connections with a number of other fields of mathematics. In the appendix, an introductory survey article is also provided for those readers unfamiliar with quantum mechanics.

American Mathematical Society eBooks•Jan 1, 2010•0 citations

Theory of Quantum Computation, Communication, and Cryptography

David Hutchison, Gerhard Weikum, Moshe Y. Vardi +14 more

Lecture notes in computer science•Jan 1, 2008•7 citations

Review of current methods of quantum and post-quantum cryptography

Мирослав Олександрович Рябий

A quantum computer can destroy most, if not all, of the traditional cryptosystems used in practice, namely, all the systems on the basis of the integer factorization problem (e. g. RSA) or the discrete logarithm problem (both traditional and elliptic curve Diffie-Hellman and DSA, and the whole cryptography based on the pairing). Some classic cryptosystems based on computationally difficult problems are very different from the above and more difficult to solve, they are independent of the quantum computation. In this paper, a review of methods of information security based on quantum and post-quantum technologies was carried out. For each of the methods of information security based on quantum technologies are the advantages and disadvantages. Describes the system of post-quantum cryptography based on lattice theory. The results of the survey allow to formalize the direction of future research of post-quantum methods and development of new effective information security systems using quantum technologies.

Ukrainian Scientific Journal of Information Security•Dec 11, 2014•0 citations

Theory of Quantum Computation, Communication, and Cryptography

Andrew M. Childs, Mosca, Michele

Lecture notes in computer science•Jan 1, 2009•32 citations
This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physical effects and computer science applications, introducing some of the main concepts and language of present day quantum information science in this context. We will mention recent developments in this new area and outline some open questions. 1. Overview Ever since the discovery of quantum mechanics people have been puzzled by the counter-intuitive character of the laws of nature. Over time we have learned to accept more and more effects that are unimaginable in a classical Newtonian world. Modern technology exploits quantum effects both to our benefit and detriment—among the memorable examples we should cite laser technology and not omit the atomic bomb. In recent years interest in quantum information theory has been generated by the prospect of employing its laws to design devices of surprising power [1]. New ideas include quantum cryptography [2, 3] and quantum computation. In 1994 Shor [4] discovered a quantum algorithm to factor numbers efficiently (that is in time that grows only polynomically with the length of the number to be factored). This has unleashed a wave of activity across a broad range of disciplines: physics, computer science, mathematics and engineering. This fruitful axis of research has uncovered many new effects that are strikingly different from their classical counterparts, both from the physical point of view as well as from a computer science and communication theory perspective. Over time these communities have gained a greater understanding of the concepts and notions of the other. The idea that information cannot be separated from
This volume is based on lectures delivered at the 2009 AMS Short Course on Quantum Computation and Quantum Information, held January 3-4, 2009, in Washington, D.C. Part I of this volume consists of two papers giving introductory surveys of many of the important topics in the newly emerging field of quantum computation and quantum information, i.e., quantum information science (QIS). The first paper discusses many of the fundamental concepts in QIS and ends with the curious and counter-intuitive phenomenon of entanglement concentration. The second gives an introductory survey of quantum error correction and fault tolerance, QIS's first line of defence against quantum decoherence. Part II consists of four papers illustrating how QIS research is currently contributing to the development of new research directions in mathematics. The first paper illustrates how differential geometry can be a fundamental research tool for the development of compilers for quantum computers. The second paper gives a survey of many of the connections between quantum topology and quantum computation. The last two papers give an overview of the new and emerging field of quantum knot theory, an interdisciplinary research field connecting quantum computation and knot theory. These two papers illustrate surprising connections with a number of other fields of mathematics. In the appendix, an introductory survey article is also provided for those readers unfamiliar with quantum mechanics.
A quantum computer can destroy most, if not all, of the traditional cryptosystems used in practice, namely, all the systems on the basis of the integer factorization problem (e. g. RSA) or the discrete logarithm problem (both traditional and elliptic curve Diffie-Hellman and DSA, and the whole cryptography based on the pairing). Some classic cryptosystems based on computationally difficult problems are very different from the above and more difficult to solve, they are independent of the quantum computation. In this paper, a review of methods of information security based on quantum and post-quantum technologies was carried out. For each of the methods of information security based on quantum technologies are the advantages and disadvantages. Describes the system of post-quantum cryptography based on lattice theory. The results of the survey allow to formalize the direction of future research of post-quantum methods and development of new effective information security systems using quantum technologies.