Related papers: Quantum transition probability in convex sets and …
The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but…
In quantum theory, the modulus-square of the inner product of two normalized Hilbert space elements is to be interpreted as the transition probability between the pure states represented by these elements. A probabilistically motivated and…
It is quite common to use the generalized probabilistic theories (GPTs) as generic models to reconstruct quantum theory from a few basic principles and to gain a better understanding of the probabilistic or information theoretic foundations…
In the years 1952 and 1965, H.-C. Wang and U. Hirzebruch showed that the two-point homogeneous compact spaces with convex metrics are isometric to the spheres, the real, complex, octonion projective spaces and the Moufang plane and as well…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
This Chapter develops a realist information-theoretic interpretation of the nonclassical features of quantum probabilities. On this view, what is fundamental in the transition from classical to quantum physics is the recognition that…
Among the many important geometric properties of quantum state space are: transitivity of the group of symmetries of the cone of unnormalized states on its interior (homogeneity), identification of this cone with its dual cone of effects…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
This paper offers a brief introduction to the framework of "general probabilistic theories", otherwise known as the "convex-operational" approach the foundations of quantum mechanics. Broadly speaking, the goal of research in this vein is…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
In the paper is discussed complete probabilistic description of quantum systems with application to multiqubit quantum computations. In simplest case it is a set of probabilities of transitions to some fixed set of states. The probabilities…
Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the latter always result from an…
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes…
I explore several related routes to deriving the Jordan-algebraic structure of finite-dimensional quantum theory from more transparent operational or physical principles, mainly involving ideas about the symmetries of, and the correlations…
We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability…
Transition probabilities are an important and useful tool in quantum mechanics. However, in their present form, they are limited in scope and only apply to pure quantum states. In this article we extend their applicability to mixed states…
This note adds to the recent spate of derivations of the probabilistic apparatus of finite-dimensional quantum theory from various axiomatic packages. We offer two different axiomatic packages that lead easily to the Jordan algebraic…