Related papers: On quantum statistics in data analysis
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
The problem of obtaining a realistic, relativistic description of a quantum system is discussed in the context of a simple (light-cone) lattice field theory. A natural stochastic model is proposed which, although non-local, is relativistic…
Complex analyses involving multiple, dependent random quantities often lead to graphical models - a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical…
Quantum statistics originate from the physics of state preparation. It is therefore wrong to think of quantum states as fundamental. In fact, quantum states are merely summaries of dynamical processes that randomize the properties of the…
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 present a quantum-like (QL) model in that contexts (complexes of e.g. mental, social, biological, economic or even political conditions) are represented by complex probability amplitudes. This approach gives the possibility to apply the…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
Bell's theorem is a statement by which averages obtained from specific types of statistical distributions must conform to a family of inequalities. These models, in accordance with the EPR argument, provide for the simultaneous existence of…
This article outlines a novel interpretation of quantum theory: the Q-based interpretation. The core idea underlying this interpretation, recently suggested for quantum field theories by Drummond and Reid [2020], is to interpret the phase…
In quantum physics the term `contextual' can be used in more than one way. One usage, here called `Bell contextual' since the idea goes back to Bell, is that if $A$, $B$ and $C$ are three quantum observables, with $A$ compatible (i.e.,…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
Physicists use quantum models to describe the behavior of physical systems. Quantum models owe their success to their interpretability, to their relation to probabilistic models (quantization of classical models) and to their high…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical…
Characterizing quantum systems through experimental data is critical to applications as diverse as metrology and quantum computing. Analyzing this experimental data in a robust and reproducible manner is made challenging, however, by the…
A projective quantum logic in terms of relative states is developed, emphasizing the importance of information transfer between a system under study and its environment. The need for accounting for the historical evolution of system is…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
We argue that the complex numbers are an irreducible object of quantum probability. This can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having complex phases as primitive ingredient…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
Observations or measurements taken of a quantum system (a small number of fundamental particles) are inherently random. If the state of the system depends on unknown parameters, then the distribution of the outcome depends on these…