Related papers: Probability Representation of Quantum Mechanics: C…

A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…

We propose the idea that in Bohmian mechanics the wavefunction is related to a density of states and explore some of its consequences. Specifically, it allows a maximum-entropy interpretation of quantum probabilities, which creates a…

The quasiprobability representation of quantum states addresses two main concerns, the identification of nonclassical features and the decomposition of the density operator. While the former aspect is a main focus of current research, the…

In this paper, we investigate a characterization of Quantum Mechanics by two physical principles based on general probabilistic theories. We first give the operationally motivated definition of the physical equivalence of states and…

The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…

Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…

It is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying instead solely on the density matrix as the description of reality. With this definition of a physical…

It is shown that probabilistic treatment of quantum mechanics can be coordinated with causality of all physical processes. The physical interpretation of quantum-mechanical phenomena such as process of measurement and collapse of quantum…

A distribution of electromagnetic fields presents a statistical assembly of a particular type, which is at scale h a quantum statistical assembly itself and has also been instrumental to concretisation of the basic probability assumption of…

The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex…

We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…

I show that probabilities in quantum mechanics are a measure of belief in the presence of human ignorance, just like all other probabilities. The Born interpretation of the square of modulus of the wave function arises from the interaction…

We present systematic proofs of statements about probability representations of qudit density states in terms of standard probability distributions of dichotomic random variables. New relations and new entropic-information inequalities are…

The quantum mechanics is considered to be a partial case of the stochastic system dynamics. It is shown that the wave function describes the state of statistically averaged system $<\mathcal{S}_{st}>$, but not that of the individual…

We present a trivial probabilistic illustration for representation of quantum mechanics as an algorithm for approximative calculation of averages.

Orthogonal decomposition of the square root of a probability density function in the Hermite basis is a useful low-dimensional parameterization of continuous probability distributions over the reals. This representation is formally similar…

The coherent and Fock states of a charge moving in varying homogeneous magnetic field are studied in the tomographic probability representation of quantum mechanics. The states are expressed in terms of quantum tomograms. The coherent…

We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability distributions and observables, with random variables. An…

A new formulation of quantum mechanics is developed which does not require the concept of the wave-particle duality. Rather than assigning probabilities to outcomes, probabilities are instead assigned to entire fine-grained histories. The…

This research applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. A tutorial-style introduction to states and various notions of the complexity of states are presented. Thereafter, the…