Inequalities in Matrix Algebras (Paperback)
Eric Carlen
Sold by CitiRetail, Stevenage, United Kingdom
AbeBooks Seller since 29 June 2022
New - Soft cover
Condition: New
Ships from United Kingdom to U.S.A.
Quantity: 1 available
Add to basketSold by CitiRetail, Stevenage, United Kingdom
AbeBooks Seller since 29 June 2022
Condition: New
Quantity: 1 available
Add to basketPaperback. The theory of positive or completely positive maps from one matrix algebra to another is the mathematical theory underlying the quantum mechanics of finite systems, as well as much of quantum information and computing. Inequalities are fundamental to the subject, and a watershed event in its development was the proof of the strong subadditivity of quantum entropy by Lieb and Ruskai. Over the next 50 years, this result has been extended and refined extensively. The development of the mathematical theory accelerated in the 1990s when researchers began to intensively investigate the quantum mechanical notion of ""entanglement"" of vectors in tensor products of Hilbert spaces. Entanglement was identified by Schrodinger as a fundamental aspect of quantum mechanics, and in recent decades questions about entanglement have led to much mathematical progress. What has emerged is a beautiful mathematical theory that has very recently arrived at a mature form. This book is an introduction to that mathematical theory, starting from modest prerequisites. A good knowledge of linear algebra and the basics of analysis and probability are sufficient. In particular, the fundamental aspects of quantum mechanics that are essential for understanding how a number of questions arose are explained from the beginning. Explore the mathematical framework underlying quantum mechanics and quantum information. Positive maps, entanglement, and key inequalities like strong subadditivity reveal decades of progress linking finite quantum systems with evolving concepts in quantum entropy, built on linear algebra, analysis, and probability. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.
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