Quantal effects and MaxEnt

Abstract

Convex operational models (COMs) are considered as great extrapolations to larger settings of any statistical theory. In this article we generalize the maximum entropy principle (MaxEnt) of Jaynes' to any COM. After expressing Max-Ent in a geometrical and latttice theoretical setting, we are able to cast it for any COM. This scope-amplification opens the door to a new systematization of the principle and sheds light into its geometrical structure. PACS numbers 03.65.Ud

Generalized Probabilities in Statistical Theories

“…• Random variables and information measures [20] will be the natural generalizations of the classical case if the event structure is not classical. A similar observation holds for the application of the MaxEnt method [111,112].…”

“…It is important to remark that many informational techniques, such as the MaxEnt method, can be suitably generalized to arbitrary probabilistic models [111,112]. In a similar vein, quantum information theory could be considered as a particular case of a generalized information theory [108].…”

Solutions for the MaxEnt problem with symmetry constraints

“…In particular, it has become very useful in quantum information theory for estimating quantum states [17,21,22]. It can also be extended to a very general family of probabilistic models [23].…”

Quantum Information as a Non-Kolmogorovian Generalization of Shannon’s Theory

“…However, these are much more general: in algebraic relativistic quantum field theory and in algebraic statistical mechanics, more general orthomodular lattices appear [32,38,39]. Many of the informational notions that can be described in quantum mechanics can be generalized to this formal setting (see, for example, [67,99,100], where the maximum entropy principle is analyzed). It is also important to mention that other types of non-Kolmogorovian probabilistic theories can be conceived of (we will not deal with them here, but see, for example, [101,102]).…”