Probability Distributions and Gleason’s Theorem
نویسندگان
چکیده
We discuss concrete examples for frame functions and their associated density operators, as well as for non-Gleason type probability measures.
منابع مشابه
An Unentangled Gleason’s Theorem
The purpose of this note is to give a generalization of Gleason’s theorem inspired by recent work in quantum information theory. For multipartite quantum systems, each of dimension three or greater, the only nonnegative frame functions over the set of unentangled states are those given by the standard Born probability rule. However, if one system is of dimension 2 this is not necessarily the case.
متن کاملA mechanistic macroscopic physical entity with a three-dimensional Hilbert space description
It is sometimes stated that Gleason’s theorem prevents the construction of hidden-variable models for quantum entities described in a more than twodimensional Hilbert space. In this paper however we explicitly construct a classical (macroscopical) system that can be represented in a threedimensional real Hilbert space, the probability structure appearing as the result of a lack of knowledge abo...
متن کاملA Bayesian Analogue of Gleason’s Theorem
We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss the use of these probabilities and we introduce a tentative generalised notion of Shannon entropy.
متن کاملModeling of Infinite Divisible Distributions Using Invariant and Equivariant Functions
Basu’s theorem is one of the most elegant results of classical statistics. Succinctly put, the theorem says: if T is a complete sufficient statistic for a family of probability measures, and V is an ancillary statistic, then T and V are independent. A very novel application of Basu’s theorem appears recently in proving the infinite divisibility of certain statistics. In addition ...
متن کاملConsistent assignment of quantum probabilities
We pose and solve a problem concerning consistent assignment of quantum probabilities to a set of bases associated with maximal projective measurements. We show that our solution is optimal. We also consider some consequences of the main theorem in the paper in conjunction with Gleason’s theorem. Some potential applications to state tomography and probabilistic quantum secret-sharing scheme are...
متن کامل