Related papers: Probability Distributions and Hilbert Spaces: Quan…
We present a general formalism for studying the effects of dynamical heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
By using a generalization of the optical tomography technique we describe the dynamics of a quantum system in terms of equations for a purely classical probability distribution which contains complete information about the system.
We present a classical probability model appropriate to the description of quantum randomness. This tool, that we have called stochastic gauge system, constitutes a contextual scheme in which the Kolmogorov probability space depends upon…
We present quantum algorithms for the loading of probability distributions using Hamiltonian simulation for one dimensional Hamiltonians of the form ${\hat H}= \Delta + V(x) \mathbb{I}$. We consider the potentials $V(x)$ for which the…
We study the possibility to describe pure quantum states and evens with classical probability distributions and conditional probabilities and show that the distributions and/or conditional probabilities have to assume negative values,…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
The tomographic probability distribution is used to decribe the kinetic equations for open quantum systems. Damped oscillator is studied. Purity parameter evolution for different damping regime is considered.
In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure…
The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but…
A method is presented to obtain local unitary invariants for multipartite quantum systems consisting of fermions or distinguishable particles. The invariants are organized into infinite families, in particular, the generalization to higher…
In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear…
Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
Any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces. This allows to decompose a quantum system into subsystems. We propose a simple tractable model for a constructive study of…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
We apply concepts of random differential geometry connected to the random matrix ensembles of the random linear operators acting on finite dimensional Hilbert spaces. The values taken by random linear operators belong to the Liouville…
We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space. We introduce the notion of Hermitian…
We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of…