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Quantum and classical systems can consistently be coupled via non-unitary time-irreversible mechanisms. In this paper we characterize which kind of corresponding dynamics converge in the stationary regime to a thermal hybrid state, that is,…
Following Ehrenfest's approach, the problem of quantum-classical correspondence can be treated in the class of trajectory-coherent functions that approximate as $\h\to 0$ a quantum-mechanical state. This idea leads to a family of systems of…
We present a consistent formalism to describe the dynamics of hybrid systems with mixed classical and quantum degrees of freedom. The probability function of the system, which, in general, will be a combination of the classical distribution…
Quantum dynamics (i.e., the Schr\"odinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid…
Quantum systems with a non-conserved probability can be described by means of non-Hermitian Hamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and…
Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. Here we extend this technique and use it to…
The extraction of classical degrees of freedom in quantum mechanics is studied in the stochastic variational method. By using this classicalization, a hybrid model constructed from quantum and classical variables (quantum-classical hybrids)…
Mixed quantum-classical dynamics is a set of methods often used to understand systems too complex to treat fully quantum mechanically. Many techniques exist for full quantum mechanical evolution on quantum computers, but mixed…
Hamiltonian theory of hybrid quantum-classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem…
The R\'enyi entanglement entropy in quantum many-body systems can be viewed as the difference in free energy between partition functions with different trace topologies. We introduce an external field $\lambda$ that controls the partition…
We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians.~Within such a framework, we study novel possible definitions of the quantum linear entropy as an…
Entropy plays a crucial role in both physics and information science, encompassing classical and quantum domains. In this work, we present the Quantum Neural Entropy Estimator (QNEE), a novel approach that combines classical neural network…
We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while…
General statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems are analyzed. It is argued that arbitrary probability densities on the hybrid phase space must be considered as the class of possible…
One of the open challenges in quantum computing is to find meaningful and practical methods to leverage quantum computation to accelerate classical machine learning workflows. A ubiquitous problem in machine learning workflows is sampling…
The relation between entanglement entropy and the computational difficulty of classically simulating Quantum Mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum…
The classical thermostatics of equilibrium processes is shown to possess a quantum-mechanical dual theory with a finite-dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the…
This work presents a general unifying theoretical framework for quantum non-equilibrium systems. It is based on a re-statement of the dynamical problem as one of inferring the distribution of collision events that move a system toward…
The $D$-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work we…
A unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous…