Related papers: Quantum Mechanical View of Mathematical Statistics
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
Given some observable H of a finite-dimensional quantum system, we investigate the typical properties of random quantum state vectors that have a fixed expectation value with respect to H. Under some some conditions on the spectrum, we…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
Quantum tomography is a process of quantum state reconstruction using data from multiple measurements. An essential goal for a quantum tomography algorithm is to find measurements that will maximize the useful information about an unknown…
We propose a general methodology for efficient statistical reconstruction of a quantum state through collection and analysis of photon counting statistics. Our approach includes both strict quantitative criteria for adequacy and…
We review the problem of state reconstruction in classical and in quantum physics, which is rarely considered at the textbook level. We review a method for retrieving a classical state in phase space, similar to that used in medical imaging…
We discuss parameter dependent polynomial ordinary differential equations that model chemical reaction networks. By classical quasi-steady state (QSS) reduction we understand the following familiar heuristic: Set the rate of change for…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
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.…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
We work out an exactly solvable hamiltonian model which retains all the features of realistic quantum measurements. In order to use an interaction process involving a system and an apparatus as a measurement, it is necessary that the…
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…
We prove a theorem showing that quantum mechanics is not directly a stochastic process characterizing Brownian motion but rather its square root. This implies that a complex-valued stochastic process is involved. Schr\"odinger equation is…
The quantum Fisher information matrix is a central object in multiparameter quantum estimation theory. It is usually challenging to obtain analytical expressions for it because most calculation methods rely on the diagonalization of the…
We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence…
The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range…
System identification is an integrant part of control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it…
Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical…
An interpretation of the probability flux is given, based on a derivation of its eigenstates and relating them to coherent state projections on a quantum wavefunction. An extended definition of the flux operator is obtained using coherent…