Quantum Information, a Survey

Frederick W. Strauch

This Resource Letter surveys the history and modern developments in the field of quantum information. It is written to guide advanced undergraduates, beginning graduate students, and other new researchers to the theoretical and experimental aspects of this field. The topics covered include quantum states and processes, quantum coding and cryptography, quantum computation, the experimental implementation of quantum information processing, and the role of quantum information in the fundamental properties and foundations of physical theories.

Gregg S. Jaeger

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.

正人 林

Masahito Hayashi

Yuanzhi Li

The no-cloning theorem has always been a hot topic in quantum theorem: As an impossibility result, this theorem precludes attempts to communicated faster than light and reinforces the security of several quantum cryptography protocol. In this survey, I will briefly introduce the history of quantum no-cloning theorem–how the thesis was invented, how did it get its name; And i would also discuss the hitherto progress on no-cloning theorem, several approach of none-perfect cloning on non-orthogonal states as well as the application of quantum no-cloning theorem in quantum cryptography and quantum information. This survey incorporates the lecture ”Quantum Information Amplifiers Beyond the No-Cloning Theorem” given by Prof. Giulio Chiribella and ”Quantum cryptography” given by Prof. Xiongfeng Ma.