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...

"Quantum Annealing: from Viewpoints of Statistical Physics, Condensed Matter Physics, and Computational Physics" (Shu Tanaka and Ryo Tamura); "Spin Glass: A Bridge between Quantum Computation and Statistical Mechanics" (Masayuki Ohzeki); and "Second Law-like Inequalities with Quantum Relative Entropy: An Introduction" (Takahiro Sagawa).