Related papers: Geometric Measures of Information for Quantum Stat…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…
We introduce a new approach to evaluating entangled quantum networks using information geometry. Quantum computing is powerful because of the enhanced correlations from quantum entanglement. For example, larger entangled networks can…
We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…
It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a…
After Shannon, entropy becomes a fundamental quantity to describe not only uncertainity or chaos of a system but also information carried by the system. Shannon's important discovery is to give a mathematical expression of the mutual…
The recent introduction of geometric partition entropy brought a new viewpoint to non-parametric entropy quantification that incorporated the impacts of informative outliers, but its original formulation was limited to the context of a…
Information-theoretic measures such as relative entropy and correlation are extremely useful when modeling or analyzing the interaction of probabilistic systems. We survey the quantum generalization of 5 such measures and point out some of…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
It is known that the high-dimensional quantum state space is notoriously complicated in contrast with the beautiful Bloch ball of the qubit. We examined the mechanism behind this fact in the frame work of general probabilistic theory (GPT),…
We take a tour of a set of equiangular lines in eight-dimensional Hilbert space. This structure defines an informationally complete measurement, that is, a way to represent all quantum states of three-qubit systems as probability…
The concept of entropy, firstly introduced in information theory, rapidly became popular in many applied sciences via Shannon's formula to measure the degree of heterogeneity among observations. A rather recent research field aims at…
The Shannon entropy of a random variable $X$ has much behaviour analogous to a signed measure. Previous work has concretized this connection by defining a signed measure $\mu$ on an abstract information space $\tilde{X}$, which is taken to…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
Inspired by works on information transmission through quantum channels, we propose the use of a couple of mutual entropies to quantify the efficiency of continual measurement schemes in extracting information on the measured quantum system.…
Relationships that exist between the classical, Shannon-type, and geometric-based approaches to sampling are investigated. Some aspects of coding and communication through a Gaussian channel are considered. In particular, a constructive…
We give an explicit expression for the geometric measure of entanglement for three qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different…
We study how information geometry is described by bulk geometry in the gauge/gravity correspondence. We consider a quantum information metric that measures the distance between the ground states of a CFT and a theory obtained by perturbing…
We present a diffeomorphism-invariant formulation of differential entropy for Riemannian spaces, providing a fine-grained, coordinate-independent notion of quantum information for continuous variables in physical space. To this end, we…
We analyze geometric terms and scaling properties of the Shannon mutual information in the continuum. This is done for a free massless scalar field theory in $d$-dimensions, in a coherent state reduced with respect to a general…
We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…