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We employ (1 + 1)-dimensional quantum cellular automata to study the evolution of entanglement and coherence near criticality in quantum systems that display nonequilibrium steady-state phase transitions. This construction permits direct access to the entire space-time structure of the underlying nonequilibrium dynamics, and allows for the analysis of unconventional correlations, such as entanglement in the time direction between the "present" and the "past." We show how the uniquely quantum part of these correlations--the coherence--can be isolated and that, close to criticality, its dynamics displays a universal power-law behavior on approach to stationarity. Focusing on quantum generalizations of classical nonequilibrium systems: the Domany-Kinzel cellular automaton and the Bagnoli-Boccara-Rechtman model, we estimate the universal critical exponents for both the entanglement and coherence. As these models belong to the one-dimensional directed percolation universality class, the latter provides a key new critical exponent, one that is unique to quantum systems. [ABSTRACT FROM AUTHOR]

Understanding quantum many-body systems with long-range or infinite-range interactions is of relevance across a broad set of physical disciplines, including quantum optics, nuclear magnetic resonance, and nuclear physics. From a theoretical viewpoint, these systems are appealing since they can be efficiently studied with numerics, and in the thermodynamic limit are expected to be governed by mean-field equations of motion. Over the past years the capabilities to experimentally create long-range interacting systems have dramatically improved permitting their control in space and time. This allows us to induce and explore a plethora of nonequilibrium dynamical phases, including time crystals and even chaotic regimes. However, establishing the emergence of these phases from numerical simulations turns out to be surprisingly challenging. This difficulty led to the assertion that mean-field theory may not be applicable to time-dependent infinite-range interacting systems. Here, we rigorously prove that mean-field theory in fact exactly captures their dynamics, in the thermodynamic limit. We further provide bounds for finite-size effects and their dependence on the evolution time.

The state of an open quantum system undergoing an adiabatic process evolves by following the instantaneous stationary state of its time-dependent generator. This observation allows one to characterize, for a generic adiabatic evolution, the average dynamics of the open system. However, information about fluctuations of dynamical observables, such as the number of photons emitted or the time-integrated stochastic entropy production in single experimental runs, requires controlling the whole spectrum of the generator and not only the stationary state. Here, we show how such information can be obtained in adiabatic open quantum dynamics by exploiting tools from large deviation theory. We prove an adiabatic theorem for deformed generators, which allows us to encode, in a biased quantum state, the full counting statistics of generic time-integrated dynamical observables. We further compute the probability associated with an arbitrary "rare" time history of the observable and derive a dynamics which realizes it in its typical behavior. Our results provide a way to characterize and engineer adiabatic open quantum dynamics and to control their fluctuations.