相关论文: Mutual Entropy in Quantum Information and Informat…
Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the…
In the context of quantum objectivity, a standard way to quantify the classicality of a state is via the mutual information between a system and different fractions of its environment. Many of the tools developed in the relevant literature…
Estimation of Shannon and R\'enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on…
The aim of this article is to provide an introduction to the use of quantum information methods for investigating the interface between quantum theory and gravity. To this end, we discuss the basic principles of two current research streams…
The first step in quantum information theory is the identification of entanglement as a valuable resource. The next step is learning how to exploit this resource efficiently. We learn how to exploit entanglement efficiently by applying…
Shannon entropy is often a quantity of interest to linguists studying the communicative capacity of human language. However, entropy must typically be estimated from observed data because researchers do not have access to the underlying…
Quantum information quantities, such as mutual information and entropies, are essential for characterizing quantum systems and protocols in quantum information science. In this contribution, we identify types of information measures based…
We review the plethora of uncertainty relations that appear in quantum mechanics and their nuances. We present both foundational applications, e.g. in understanding and defining complementarity, and practical applications, e.g. in quantum…
We investigate the quantum information by a theoretical measurement approach of an Aharanov-Bohm (AB) ring with Yukawa interaction in curved space with disclination. It obtained the so-called Shannon entropy, through the eigenfunctions of…
We study the quantum entropy of systems that are described by general non-Hermitian Hamiltonians, including those which can model the effects of sinks or sources. We generalize the von Neumann entropy to the non- Hermitian case and find…
It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…
We introduce a new quantity to petrology, the Shannon entropy, as a tool for quantifying mixing as well as the rate of production of hybrid compositions in the mixing system. The Shannon entropy approach is applied to time series numerical…
Information theory is a statistical theory dealing with the relative state of detectors and physical systems. Because of this physicality of information, the classical framework of Shannon needs to be extended to deal with quantum…
Entropy measures quantify the amount of information and correlation present in a quantum system. In practice, when the quantum state is unknown and only copies thereof are available, one must resort to the estimation of such entropy…
Information-theoretic quantities, such as entropy, are used to quantify the amount of information a given variable provides. Entropies can be used together to compute the mutual information, which quantifies the amount of information two…
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\'{e}nyi entropy and its related entropy power. This…
A natural measure for the amount of quantum information that a physical system E holds about another system A = A_1,...,A_n is given by the min-entropy Hmin(A|E). Specifically, the min-entropy measures the amount of entanglement between E…
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…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…
Information theory is introduced in this lecture note with a particular emphasis on its relevance to algebraic coding theory. The document develops the mathematical foundations for quantifying uncertainty and information transmission by…