The Functional Analysis of Quantum Information Theory

Livro digital

Título:
The Functional Analysis of Quantum Information Theory

Autor:
Ved Prakash Gupta, Prabha Mandayam, V. S. Sunder

Categoria:
Tecnologia > IA

Doador:
Raffaello D. N.

Sinopse:
Quantum information theory sits at a triple junction of physics, computer science, and mathematics. This book attacks it from the mathematical side, applying the tools of functional analysis—operator spaces, completely bounded maps, and operator systems—to the foundations of quantum information. Derived from a two-week workshop at the Institute of Mathematical Sciences in Chennai, it transcribes lectures by four leading researchers: Gilles Pisier, K. R. Parthasarathy, Vern Paulsen, and Andreas Winter. The notes develop the mathematical scaffolding rigorously. Early chapters establish operator space theory and the fundamental factorization of completely bounded maps. Later sections deploy these tools on concrete quantum information problems: entanglement measures, channel capacities, and the structure of quantum correlations. The Kraus decomposition appears multiple times from different angles—a feature, not a bug, for readers who benefit from seeing the same object refracted through distinct mathematical lenses. This is not a textbook for a first encounter with quantum information. It assumes comfort with functional analysis and operator algebras, and it rewards readers who bring that background. For mathematicians curious about what their tools can say about qubits, or for quantum information theorists who sense they are missing the functional-analytic big picture, it fills a gap few other resources address.