Related papers: Quantum Mechanics of Stochastic Systems
The quantum states representing classical phase space are given, and these are used to formulate quantum statistical mechanics as a formally exact double perturbation expansion about classical statistical mechanics. One series of quantum…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
This paper investigates dynamical relaxation to quantum equilibrium in the stochastic de Broglie-Bohm-Bell formulation of quantum mechanics. The time-dependent probability distributions are computed as in a Markov process with slowly…
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…
If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below.…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
In this work, we aim at augmenting the decisions output by quantum models with "error bars" that provide finite-sample coverage guarantees. Quantum models implement implicit probabilistic predictors that produce multiple random decisions…
A system of quantum reasoning for a closed system is developed by treating non-relativistic quantum mechanics as a stochastic theory. The sample space corresponds to a decomposition, as a sum of orthogonal projectors, of the identity…
It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation…
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
Identical systems, or entities, are indistinguishable in quantum mechanics (QM), and the symmetrization postulate rules the possible statistical distributions of a large number of identical quantum entities. However, a thorough analysis 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…
Quantum coherence serves as a fundamental resource for generating intrinsic randomness, yet the quantification of randomness in quantum random number generators (QRNGs) based on spontaneous emission has remained largely phenomenological.…
We provide a formulation of quantum mechanics based on the cohomology of the Batalin-Vilkovisky (BV) algebra. Focusing on quantum-mechanical systems without gauge symmetry we introduce a homotopy retract from the chain complex of the…
Physical potentials are routinely approximated to harmonic potentials so as to analytically solve the system dynamics. Often it is important to know when a quantum harmonic oscillator (QHO) behaves quantum mechanically and when classically.…
Quantum estimation theory is a reformulation of random statistical theory with the modern language of quantum mechanics. In fact, the density operator plays a role similar to that of probability distribution functions in classical…
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level…