This book is a collection of lecture notes/contributions from a summer school on decoherence, entanglement & entropy and a workshop on MPS (matrix product states) & DMRG (density matrix renormalization group). Subjects of the summer school include introduction to MPS, black holes, qubits and octonions, weak measurement, entanglement measures and separability, generalized Bell inequalities, among others. Subjects of the workshop are dedicated to MPS and DMRG. Applications to strongly correlated systems and integrable systems are also mentioned. Contributions to this book are prepared in a self-contained manner so that a reader with a modest background in quantum information and quantum computing may understand the subjects.
Black Holes and Qubits; Weak Value with Decoherence; Lectures on Matrix Product Representation of States; On a Possible Definition of Entanglement in Antisymmetric States; Entanglement Measures for Intermediate Separability; Unruh Effect on Quantum Teleportation and Entanglement: Implications on Black Hole Information; Systematic Construction of Generalized Bell Inequalities; On 3-variable Exponential Polynomials and Quantum Algorithms; Application of Density Matrix Renormalization Group Method to Photoinduced Phenomena in Strongly Correlated Electron Systems; Density-Matrix Renormalization Group Method for Tomonaga-Luttinger Liquid; Supersymmetric Valence-Bond Solid Models - Hidden Order and Dynamics; Matrix Product States in Quantum Integrable Models; A Systematic Way to Find and Construct Exact Finite Dimensional Matrix Product Stationary States.