Related papers: A Universal Representation for Quantum Commuting C…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
Motivated by Quantum Bayesianism I give background for a general epistemic approach to quantum mechanics, where complementarity and symmetry are the only essential features. A general definition of a symmetric epistemic setting is…
In this note, we consider quantum correlations of bipartite systems having a slight interaction, and reinterpret Tsirelson's problem (and hence Kirchberg's and Connes's conjectures) in terms of finite-dimensional asymptotically commuting…
The aim of the present paper is to introduce and to discuss the most basic fundamental concepts of quantum physics by means of a simple and pedagogical example. An appreciable part of its content presents original results. We start with the…
Quantum logic aims to capture essential quantum mechanical structure in order-theoretic terms. The Achilles' heel of quantum logic is the absence of a canonical description of composite systems, given descriptions of their components. We…
An abstract formulation of quantum dynamics in the presence of a general set of quantum constraints is developed. Our constructive procedure is such that the relevant projection operator onto the physical Hilbert space is obtained with a…
(2+2)-dimensional quantum mechanical q-phase space which is the semi-direct product of the quantum plane E_q(2)/U(1) and its dual algebra e_q(2)/u(1) is constructed. Commutation and the resulting uncertainty relations are studied. ``Quantum…
We derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The basic setting is a set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$ on the…
We illustrate an isomorphic representation of the observable algebra for quantum mechanics in terms of the functions on the projective Hilbert space, and its Hilbert space analog, with a noncommutative product in terms of explicit…
We define a "quantum relation" on a von Neumann algebra M \subset B(H) to be a weak* closed operator bimodule over its commutant M'. Although this definition is framed in terms of a particular representation of M, it is effectively…
A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability of the Hermitian quadratic form, the direct integral structure of…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
A definition of quantum correlation is presented for an arbitrary bipartite quantum state based on the skew information. This definition not only inherits the good properties of skew information such as the contractivity and so on, but also…
This note is an introduction to methods of construction for Hilbert space realizations of relativistic quantum physics. The realizations satisfy a revision to Wightman's functional analytic axioms and exhibit interaction in physical…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is…
The Hermiticity condition in quantum mechanics required for the characterisation of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose…
We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is…
The ultimate miniaturization of electronic devices will likely require local and coherent control of single electronic wavefunctions. Wavefunctions exist within both physical real space and an abstract state space with a simple geometric…
A finite shift plane can be equivalently defined via abelian relative difference sets as well as planar functions. In this paper, we present a generic way to construct unitals in finite shift planes of odd orders $q^2$. We investigate…