Quantifying Structure and Information Processing in One-Dimensional Quantum Systems

We develop a framework for studying one-dimensional quantum systems with stationary, ergodic dynamics and introduce quantum information properties related to the von Neumann entropies of blocks of qubits within a structured chain. Some of the resulting statistical features are unique to quantum systems and others can be recreated with purely classical ensembles. Applying sequential measurements on these quantum states yields classical stochastic processes whose information properties are determined by the structure of the initial quantum state and the measurement protocol. Examples states with short- and long-range entanglement, as well as specific Hamiltonian ground states are analyzed within this framework.