Quantum and classical temporal correlations in $(1+1)D$ Quantum Cellular Automata

Abstract

We employ $(1+1)$-dimensional quantum cellular automata to study the evolution of entanglement and coherence near criticality in quantum systems that display non-equilibrium steady-state phase transitions. This construction permits direct access to the entire space-time structure of the underlying non-equilibrium dynamics. It contains the full ensemble of classical trajectories and also allows for the analysis of unconventional correlations, such as entanglement in the time direction between the "present" and the "past". Close to criticality, the dynamics of these correlations - which we quantify through the second-order Renyi entropy - displays power-law behavior on its approach to stationarity. Our analysis is based on quantum generalizations of classical non-equilibrium systems: the Domany-Kinzel cellular automaton and the Bagnoli-Boccara-Rechtman model, for which we provide estimates for the critical exponents related to the classical and quantum components of the entropy. Our study shows that $(1+1)$-dimensional quantum cellular automata permit an intriguing perspective on the nature of classical and quantum correlations in out-of-equilibrium systems.

5 pages, 2 figures. Supplementary Material of 7 pages, 2 figures

References in corpus (6)

• The density-matrix renormalization group in the age of matrix product states
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Directed percolation criticality in turbulent liquid crystals
• Non-equilibrium effective field theory for absorbing state phase transitions in driven open quantum spin systems
• Nonequilibrium phase transition in an open quantum spin system with long-range interaction
• Tricritical directed percolation with long-range interaction in one and two dimensions

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