Quantum Ergodic Channels in Operator Algebras

Насир Набиевич Ганиходжаев, Farrukh Maksutovich Mukhamedov

József Zsolt Bernád

Iterates of quantum operations and their convergence are investigated in the context of mean ergodic theory. We discuss in detail the convergence of the iterates and show that the uniform ergodic theorem plays an essential role. Our results will follow from some general theorems concerning completely positive maps, mean ergodic operators, and operator algebras on Hilbert spaces. A few examples of both finite and infinite dimensional Hilbert spaces are presented as well.

Th.J. Siskens, Peter Bongaarts

Marcell D. Kovács, Christopher J. Turner, Lluís Masanes

Finding analytically tractable model systems for quantum ergodicity breaking in interacting systems remains a theoretical challenge. This paper presents an algebraic theory of robust ergodicity breaking in time-periodic unitary circuits under local causal constraints. Our model is based on constructing tripartite unitaries (we dub 'walls') that permanently arrest local operator spreading. We show that the structure of the resulting causally independent subsystems can be understood rigorously through the invariance of embedded operator algebras (i.e. super-operator symmetries). This formalism gives a natural identification of local conserved quantities and permits the generalisation to time-dependent dynamics. Using representation theory, the general form of unitaries exhibiting causal decoupling is derived from the automorphism group of the embedded algebra with links to quantum error-correcting codes. From the point of view of operator spreading, our theory is a minimal model for non-ergodic quantum-circuit dynamics, and we explore its effects on probes of many-body quantum chaos. We prove an entanglement area law due to causal constraints and discuss its stability against local measurements. In a random unitary ensemble with causally independent subsystems, we compare spectral correlations with those of the universal random matrix ensemble using the spectral form factor. Our results offer a rigorous understanding of locally constrained quantum dynamics from a quantum information perspective.

Th.J. Siskens, Peter Bongaarts

Noborn Watanabe

Adaptive Dynamics and Its Applications to Chaos and NPC Problem Quantum Algorithm for SAT Problem and Quantum Mutual Entropy New Quantum Algorithm for Studying NP-Complete Problems Entanglement, Quantum Entropy and Mutual Information Fundamentals of Quantum Mutual Entropy and Capacity Compound Channels, Transition Expectations, and Liftings Complexities and Their Applications to Characterization of Chaos Complexity, Fractal Dimension for Quantum States Information Dynamics and Its Applications to Optical Communication Processes Information Theoretical Treatments of Genes Some Aspects of Quantum Information Theory and Their Applications to Irreversible Processes On Compound State and Mutual Information in Quantum Information Theory Note on Quantum Probability Quantum Ergodic Channels in Operator Algebras On Open System Dynamics -- An Operator Algebraic Study Dynamical Process in Linear Response Theory Stability of Weiss Ising Model and other papers.