Gacs Algorithmic Complexity on Hilbert Spaces and Some of its Applications (1511.00635v1)

Abstract: We extend the notion of Gacs quantum algorithmic entropy, originally formulated for finitely many qubits, to infinite dimensional quantum spin chains and investigate the relation of this extension with two quantum dynamical entropies that have been proposed in recent years. Further, we prove an extension of Brudno's theorem in quantum spin chains with shift dynamics.