Related papers: Information Theory and Quadrature Rules
We provide explicit expressions for quadrature rules on the space of $C^1$ quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention…
In this paper and a companion paper, we attempt to systematically investigate the possibility that the concept of information may enable a derivation of the quantum formalism from a set of physically comprehensible postulates. To do so, we…
The classic concept of "calibrated forecasts" and its more recent refinement, "calibeating," are defined with respect to the standard quadratic scoring rule. We extend these notions to the class of $\textit{proper}$ scoring rules (for which…
We introduce a uniform representation of general objects that captures the regularities with respect to their structure. It allows a representation of a general class of objects including geometric patterns and images in a sparse, modular,…
In modern quantum information theory one deals with an idealized situation when the spacetime dependence of quantum phenomena is neglected. However the transmission and processing of (quantum) information is a physical process in spacetime.…
In this paper we investigate stopping criteria for iterative decoding from a mutual information perspective. We introduce new iteration stopping rules based on an approximation of the mutual information between encoded bits and decoder soft…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played by quantities such as various order parameters,…
A high-order quadrature algorithm is presented for computing integrals over curved surfaces and volumes whose geometry is implicitly defined by the level sets of (one or more) multivariate polynomials. The algorithm recasts the implicitly…
Corrected trapezoidal rules are proved for $\int_a^b f(x)\,dx$ under the assumption that $f"\in L^p([a,b])$ for some $1\leq p\leq\infty$. Such quadrature rules involve the trapezoidal rule modified by the addition of a term…
The phase shift rules enable the estimation of the derivative of a quantum state with respect to phase parameters, providing valuable insights into the behavior and dynamics of quantum systems. This capability is essential in quantum…
Quantum experiments yield random data. We show that the most efficient way to store this empirical information by a finite number of bits is by means of the vector of square roots of observed relative frequencies. This vector has the unique…
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…
Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to…
A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to…
A novel mathematical framework is derived for the addition of nodes to univariate and interpolatory quadrature rules. The framework is based on the geometrical interpretation of the Vandermonde matrix describing the relation between the…
Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system's ability to…
Random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), found applications in literature in study of following quantum…
We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…
This paper presents algorithms for calculating the quadratic character and the norms of prime ideals in the ring of integers of any quadratic field. The norms of prime ideals are obtained by means of a sieve algorithm using the quadratic…