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Discrete-time quantum walks provide a natural framework for quantum transport on complex networks. On regular structures, coin-walker entanglement has been widely used to characterize quantum transport and to support quantum algorithmic…
In this paper we remark that Shannon entropy can be expressed as a function of the self-information (i.e. the logarithm) and the inverse of the Lambert $W$ function. It means that we consider that Shannon entropy has the trace form: $-k…
We provide a general description of the phenomenon of entanglement in bipartite systems, as it manifests in micro and macro physical systems, as well as in human cognitive processes. We do so by observing that when genuine coincidence…
Using the concept of von Neumann entropy, we quantify the information content of the various components of the quantum walk system, including the mutual information between its subsystems (coin and position) and use it to give a precise…
Our aim is to make a step towards clarification of foundations for the notion of entanglement (both physical and mathematical) by representing it in the conditional probability framework. In Schr\"odinger's words, this is entanglement of…
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,…
Monitored many-body systems fall broadly into two dynamical phases, ``entangling'' or ``disentangling'', separated by a transition as a function of the rate at which measurements are made on the system. Producing an analytical theory of…
We present a mathematical construction of new quantum information measures that generalize the notion of logarithmic negativity. Our approach is based on formal group theory. We shall prove that this family of generalized negativity…
A quantum many-body system whose dynamics includes local measurements at a nonzero rate can be in distinct dynamical phases, with differing entanglement properties. We introduce theoretical approaches to measurement-induced phase…
We describe an efficient theoretical criterion, suitable for indistinguishable particles to quantify the quantum correlations of any pure two-fermion state, based on the Slater rank concept. It represents the natural generalization of the…
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…
The participation coefficient is a widely used metric of the diversity of a node's connections with respect to a modular partition of a network. An information-theoretic formulation of this concept of connection diversity, referred to here…
I give an overview of some of the most used measures of entanglement. To make the presentation self-contained, a number of concepts from quantum information theory are first explained. Then the structure of bipartite entanglement is studied…
Understanding a complex system entails capturing the non-trivial collective phenomena that arise from interactions between its different parts. Information theory is a flexible and robust framework to study such behaviours, with several…
This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other…
The purpose of this paper is to study entanglement of quantum states by means of Schmidt decomposition. The notion of Schmidt information which characterizes the non-randomness of correlations between two observers that conduct measurements…
Many of the traditional results in information theory, such as the channel coding theorem or the source coding theorem, are restricted to scenarios where the underlying resources are independent and identically distributed (i.i.d.) over a…
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability…
A new paradigm for distributed quantum systems where information is a valuable resource is developed. After finding a unique measure for information, we construct a scheme for it's manipulation in analogy with entanglement theory. In this…
A tree tensor network variational method is proposed to simulate quantum many-body systems with global symmetries where the optimization is reduced to individual charge configurations. A computational scheme is presented, how to extract the…