Related papers: Relative entropy in quantum information theory
Many important quantities in quantum information science, such as entropy and entanglement, are non-linear functions of the density matrix and cannot be expressed as operator observables. Standard open-system approaches evolve only a single…
We introduce the use of entanglement entropy as a tool for studying the amount of information shared between the nodes of quantum complex networks. By considering the ground state of a network of coupled quantum harmonic oscillators, we…
The theory of noncommutative dynamical entropy and quantum symbolic dynamics for quantum dynamical systems is analised from the point of view of quantum information theory. Using a general quantum dynamical system as a communication channel…
This is a review on entropy in various fields of mathematics and science. Its scope is to convey a unified vision of the classical as well as some newer entropy notions to a broad audience with an intermediate background in dynamical…
This thesis establishes a number of connections between foundational issues in quantum theory, and some quantum information applications. It starts with a review of quantum contextuality and non-locality, multipartite entanglement…
A new interpretation of entanglement entropy is proposed: entanglement entropy of a pure state with respect to a division of a Hilbert space into two subspaces 1 and 2 is an amount of information, which can be transmitted through 1 and 2…
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this…
We describe some applications of quantum information theory to the analysis of quantum limits on measurement sensitivity. A measurement of a weak force acting on a quantum system is a determination of a classical parameter appearing in the…
Finding the minimal relative entropy of two quantum states under semidefinite constraints is a pivotal problem located at the mathematical core of various applications in quantum information theory. An efficient method for providing…
Uncertainty relations take a crucial and fundamental part in the frame of quantum theory, and are bringing on many marvelous applications in the emerging field of quantum information sciences. Especially, as entropy is imposed into the…
The novel concept of quantum logical entropy is presented and analyzed. We prove several basic properties of this entropy with regard to density matrices. We hereby motivate a different approach for the assignment of quantum entropy to…
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…
Information theory has become an increasingly important research field to better understand quantum mechanics. Noteworthy, it covers both foundational and applied perspectives, also offering a common technical language to study a variety of…
In this Thesis, several results in quantum information theory are collected, most of which use entropy as the main mathematical tool. *While a direct generalization of the Shannon entropy to density matrices, the von Neumann entropy behaves…
Short review on entanglement, as seen from a quantum information perspective, and some simple applications to many-body quantum systems. Special emphasis in area laws, cold atoms, and efficient descriptions using tensor network states.
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 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…
This thesis covers several aspects of entanglement in the context of quantum information theory.
We study entanglement entropy in gravity theory with quantum effects. A simplest model is a two dimensional Einstein-Hilbert action . We use an $n$-sheet manifold to obtain an area term of entanglement entropy by summing over all background…
Many quantum information theoretic quantities are similar to and/or inspired by thermodynamic quantities, with entanglement entropy being a well-known example. In this paper, we study a less well-known example, capacity of entanglement,…