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Formal development of the mathematical theory of quantum information with clear proofs and exercises. For graduate students and researchers.
This largely self-contained book on the theory of quantum information focuses on precise mathematical formulations and proofs of fundamental facts that form the foundation of the subject. It is intended for graduate students and researchers in mathematics, computer science, and theoretical physics seeking to develop a thorough understanding of key results, proof techniques, and methodologies that are relevant to a wide range of research topics within the theory of quantum information and computation. The book is accessible to readers with an understanding of basic mathematics, including linear algebra, mathematical analysis, and probability theory. An introductory chapter summarizes these necessary mathematical prerequisites, and starting from this foundation, the book includes clear and complete proofs of all results it presents. Each subsequent chapter includes challenging exercises intended to help readers to develop their own skills for discovering proofs concerning the theory of quantum information.
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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.
On 13 August 1990 members of the Mille Lacs Band of Ojibwe filed a lawsuit against the State of Minnesota for interfering with the hunting, fishing, and gathering rights that had been guaranteed to them in an 1837 treaty with the United States. In order to interpret the treaty the courts had to consider historical circumstances, the intentions of the parties, and the treaty's implementation. The Mille Lacs Band faced a mammoth challenge. How does one argue the Native side of the case when all historical documentation was written by non- Natives? The Mille Lacs selected six scholars to testify for them. Published here for the first time, Charles Cleland, James McClurken, Helen Tanner, John Nichols, Thomas Lund, and Bruce White discuss the circumstances under which the treaty was written, the personalities involved in the negotiations and the legal rhetoric of the times, as well as analyze related legal conflicts between Natives and non- Natives. Justice Sandra Day O'Connor delivered the 1999 Opinion of the [United States Supreme] Court.
Beginning in 1924, Proceedings are incorporated into the Apr. number.