相关论文: Entropic Geometry from Logic

The relative entropy of two n-party quantum states is an important quantity exhibiting, for example, the extent to which the two states are different. The relative entropy of the states formed by reducing two n-party to a smaller number $m$…

We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…

These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…

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…

Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…

Entropy is a famous and well established concept in physics and engineering that can be used for explanation of basic fundamentals as well it finds applications in several areas, from quantum physics to astronomy, from network communication…

Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…

The paper analyzes the probability distribution of the occupancy numbers and the entropy of a system at the equilibrium composed by an arbitrary number of non-interacting bosons. The probability distribution is derived both by tracing out…

Entropy is a concept that has traditionally been reliant on a definite notion of causality. However, without a definite notion of causality, the concept of entropy is not all lost. Indefinite causal structure results from combining…

Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…

The general framework of Entropic Dynamics (ED) is used to construct non-relativistic models of relational quantum mechanics from well known inference principles -- probability, entropy and information geometry. Although only partially…

The entropy region is constructed from vectors of random variables by collecting Shannon entropies of all subvectors. Its shape is studied here by means of polymatroidal constructions, notably by convolution. The closure of the region is…

The general framework of entropic dynamics is used to formulate a relational quantum dynamics. The main new idea is to use tools of information geometry to develop an entropic measure of the mismatch between successive configurations of a…

The geometric entanglement entropy of a quantum field in the vacuum state is known to be divergent and, when regularized, to scale as the area of the boundary of the region. Here we introduce an operational definition of the entropy of the…

Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…

A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…

The entropy region is a fundamental object in information theory. An outer bound for the entropy region is defined by a minimal set of Shannon-type inequalities called elemental inequalities also referred to as the Shannon region. This…

Given any finite set equipped with a probability measure, one may compute its Shannon entropy or information content. The entropy becomes the logarithm of the cardinality of the set when the uniform probability is used. Leinster introduced…

There are two main approach to probability, one of set-theoretic character where probability is the measure of a set, and another one of linguistic character where probability is the degree of confidence in a proposition. In this work we…

Logical probability theory was developed as a quantitative measure based on Boole's logic of subsets. But information theory was developed into a mature theory by Claude Shannon with no such connection to logic. A recent development in…