Related papers: A Complexity-Based Approach to Quantum Observable …
We demonstrate equilibration of isolated many-body systems in the sense that, after initial transients have died out, the system behaves practically indistinguishable from a time-independent steady state, i.e., non-negligible deviations are…
When quantifying the mixing properties of a quantum dynamical system in terms of dynamical entropy, the following scheme appears natural: observe the state of the system at regular time intervals while it evolves and determine the entropy…
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a…
We investigate different measures of stability of quantum statistical ensembles with respect to local measurements. We call a quantum statistical ensemble "stable" if a small number of local measurements cannot significantly modify the…
In this work, we introduce an information-theoretic approach for considering changes in dynamics of finitely dimensional open quantum systems governed by master equations. This experimentally motivated approach arises from considering how…
An alternative approach to decoherence, named non-dynamical decoherence is developed and used to resolve the quantum measurement problem. According to decoherence, the observed system is open to a macroscopic apparatus(together with a…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…
We provide a detailed comparison between the dynamics of high-temperature spatiotemporal correlation functions in quantum and classical spin models. In the quantum case, our large-scale numerics are based on the concept of quantum…
In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second…
Quantum machine learning (QML) holds promise for accelerating pattern recognition, optimization, and data analysis, but the conditions under which it can truly outperform classical approaches remain unclear. Existing research often…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides a new operator-theoretic representation of classical dynamics by combining ergodic theory with quantum…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…
In a partially observed quantum or classical system the information that we cannot access results in our description of the system becoming mixed even if we have perfect initial knowledge. That is, if the system is quantum the conditional…
Quantum state estimation, based on the numerical integration of stochastic master equations (SMEs), provides estimates for the evolution of quantum systems subject to continuous weak measurements. The approach is similar to classical state…
A nonequilibrium statistical operator method is developed for ensembles of particles obeying non-Hamiltonian equations of motion in classical phase space. The main consequences of non-zero compressibility of phase space are examined in…
Following a review of quantum-classical hybrid dynamics, we discuss the ensuing proliferation of observables and relate it to measurements of (would-be) quantum mechanical degrees of freedom performed by (would-be) classical ones (if they…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
We investigate the role of coherence and Markovianity in finding an answer to the question whether the outcomes of a projectively measured quantum stochastic process are compatible with a classical stochastic process. For this purpose we…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…