Related papers: On classical and quantum liftings
This note shows how quantum entanglement may be simulated in classical computing. The simulated entanglement protocol is implemented using oblivious transfer in the simplest case and other many-to-one mappings in more general cases. For the…
We consider quantum and classical first-order transitions, at equilibrium and under out-of-equilibrium conditions, mainly focusing on quench and slow quasi-adiabatic protocols. For these phenomena, we review the finite-size scaling theory…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
We show how to use operators in the description of {\em exchanging processes} often taking place in (complex) classical systems. In particular, we propose a set of rules giving rise to an {\em hamiltonian} operator for such a system $\Sc$,…
The purpose of this paper is two-fold. First, to make clear (and de-mystify) the basic concepts of classical thermodynamics, and thus to enable the integration of thermodynamics within systems modeling and control. Second, to demonstrate…
In this paper, we analyze classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open or closed-loop feedback evolution of a control…
Reservoir computing is a versatile paradigm in computational neuroscience and machine learning, that exploits the non-linear dynamics of a dynamical system - the reservoir - to efficiently process time-dependent information. Since its…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
A filtering problem for a class of quantum systems disturbed by a classical stochastic process is investigated in this paper. The classical disturbance process, which is assumed to be described by a linear stochastic differential equation,…
We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian)…
We show how quantum dynamics can be captured in the state of a quantum system, in such a way that the system can be used to stochastically perform, at a later time, the stored transformation perfectly on some other quantum system. Thus…
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
We propose in this work a concept of integrability for quantum systems, which corresponds to the concept of noncommutative integrability for systems in classical mechanics. We determine a condition for quantum operators which can be a…
This contribution analyses the classical laws of motion by means of an approach relating time and entropy. We argue that adopting the notion of change of states as opposed to the usual derivation of Newton's laws in terms of fields a…
The interplay between classical and quantum mechanical evolution in the optical centrifuge (OC) is discussed. The analysis is based on the quantum mechanical formalism starting from either the ground state or a thermal ensemble. Two…
This work originates from part of a final year undergraduate research project on the Eisenhart lift for Hamiltonian systems. The Eisenhart lift is a procedure to describe trajectories of a classical natural Hamiltonian system as geodesics…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
The purpose of this paper is to show how a class of classical linear stochastic systems can be physically implemented using quantum optical components. Quantum optical systems typically have much higher bandwidth than electronic devices,…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…