Related papers: Probability representation of quantum evolution an…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
In the framework of the Heisenberg picture, an alternative derivation of the reduced density matrix of a driven dissipative quantum harmonic oscillator as the prototype of an open quantum system is investigated. The reduced density matrix…
We introduce a numerical method to simulate nonlinear open quantum dynamics of a particle in situations where its state undergoes significant expansion in phase space while generating small quantum features at the phase-space Planck scale.…
Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a…
The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation…
The quantum measurement problem considered for the model of measuring system (MS) consist of measured state S (particle), detector D and information processing device (observer) $O$ interacting with S,D. For 'external' observer $O'$ MS…
Tomography of a quantum state is usually based on positive operator-valued measure (POVM) and on their experimental statistics. Among the available reconstructions, the maximum-likelihood (MaxLike) technique is an efficient one. We propose…
The probability representation of quantum and classical statistical mechanics is discussed. Symplectic tomography, center-of-mass tomography, and spin tomography are studied. The connection of tomographic probabilities with dynamic…
The probability operator is derived from first principles for an equilibrium quantum system. It is also shown that the superposition states collapse into a mixture of states giving the conventional von Neumann trace form for the quantum…
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
We describe fermions in terms of a classical statistical ensemble. The states $\tau$ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability…
Utilizing the tools of quantum optics to prepare and manipulate quantum states of motion of a mechanical resonator is currently one of the most promising routes to explore non-classicality at a macroscopic scale. An important quantum…
We analyse the quantum evolution of a particle moving in a potential in interaction with an environment of harmonic oscillators in a thermal state, using the quantum state diffusion (QSD) picture of Gisin and Percival, in which one…
The formalism of generalized Wigner transformations developped in a previous paper, is applied to kinetic equations of the Lindblad type for quantum harmonic oscillator models. It is first applied to an oscillator coupled to an equilibrium…
Stochastic differential equations for processes with values in Hilbert spaces are now largely used in the quantum theory of open systems. In this work we present a class of such equations and discuss their main properties; moreover, we…
We derive a well-behaved nonlinear extension of the non-relativistic Liouville-von Neumann dynamics driven by maximal entropy production with conservation of energy and probability. The pure state limit reduces to the usual Schroedinger…
Starting from a new principle inspired by quantum tomography rather than from Born's rule, this paper gives a self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum…
Unbounded potentials are always utilized to strictly confine quantum dynamics and generate bound or stationary states due to the existence of quantum tunneling. However, the existed accurate Wigner solvers are often designed for either…
The excitation of atomic and molecular systems by propagating light in a two-photon state within the Wigner-Weisskopf approximation has been described using stochastic tools. The problem of a stochastic evolution of the quantum system,…
The question of the representation of quantum stationary partially polarized waves as random superpositions of different polarization ellipses is addressed. To this end, the Bohmian formulation of quantum mechanics is considered and…