Related papers: Quantum Mechanics of Stochastic Systems

A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…

We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as…

Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt,…

An extension of the Born rule, the {\it quantum typicality rule}, has recently been proposed [B. Galvan: Found. Phys. 37, 1540-1562 (2007)]. Roughly speaking, this rule states that if the wave function of a particle is split into…

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…

Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…

Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement which excludes in principle the singular direct observability continual case. Quantum theory of time continuous measurements and quantum prediction…

Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…

Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…

We deal with the general structure of (noncommutative) stochastic processes by using the standard techniques of Operator Algebras. Any stochastic process is associated to a state on a universal object, i.e. the free product $C^*$-algebra in…

Statistically interpretable axioms are formulated that define a quantum stochastic process (QSP) as a causally ordered operator field in an arbitrary space-time region T of an open quantum system under a sequential observation at a discrete…

This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…

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…

The one particle quantum mechanics is considered in the frame of a N-body classical kinetics in the phase space. Within this framework, the scenario of a subquantum structure for the quantum particle, emerges naturally, providing an…

Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing…

We present a fully digital framework that replicates the statistical behavior of coherent-state quantum random number generation (QRNG) by harnessing system timing jitter through random permutation processes. Our approach transforms…

We sketch a quantum mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the quasiclassical domain of familiar experience and for…

We propose a quantum algorithm for sampling from a solution of stochastic differential equations (SDEs). Using differentiable quantum circuits (DQCs) with a feature map encoding of latent variables, we represent the quantile function for an…

In this work, we consider a probability representation of quantum dynamics for finite-dimensional quantum systems with the use of pseudostochastic maps acting on true probability distributions. These probability distributions are obtained…

We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…