Related papers: Symplectic tomography as classical approach to qua…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In…
An assessment is given as to the extent to which pure unitary evolution, as distinct from environmental decohering interaction, can provide the transition necessary for an observer to interpret perceived quantum dynamics as classical. This…
We give an overview of the two different methods that have been introduced in order to describe the dynamics of constrained quantum systems; the symplectic formulation and the metric formulation. The symplectic method extends the work of…
The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic…
We develop a universal approach enabling the study of any multimode quantum optical system evolving under a quadratic Hamiltonian. Our strategy generalizes the standard symplectic analysis and permits the treatment of multimode systems even…
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time ). The…
A sample of some relevant developments that have taken place during the last twenty years in classical and quantum tomography are displayed. We will present a general conceptual framework that provides a simple unifying mathematical picture…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
In this job, we will present a theory called Quantum Tomography that is the natural extension of the theory of detection of signals in classical telecommunications to Quantum Mechanics. This theory mainly consists in the reconstruction of a…
A review of the tomographic-probability representation of classical and quantum states is presented. The tomographic entropies and entropic uncertainty relations are discussed in connection with ambiguities in the interpretation of the…
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
Severe methodological and numerical problems of the traditional quantum mechanical approach to the description of molecular systems are outlined. To overcome these, a simple alternative to the Born-Oppenheimer approximation is presented on…
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general…
We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
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.…