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). It is prepared in a self-contained manner so that readers with a modest background in quantum information and quantum computing may understand.

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.