How can one prove that a given quantum state is entangled? In this paper we review
different methods that have been proposed for entanglement detection. We first explain the …

In this paper we give a self-contained introduction to the conceptional and mathematical
foundations of quantum information theory. In the first part we introduce the basic notions …

Quantum information theory is a branch of science at the frontier of physics, mathematics,
and information science, and offers a variety of solutions that are impossible using classical …

Einstein-Podolsky-Rosen steering is a form of bipartite quantum correlation that is
intermediate between entanglement and Bell nonlocality. It allows for entanglement …

Physical Relativity explores the nature of the distinction at the heart of Einstein's 1905
formulation of his special theory of relativity: that between kinematics and dynamics. Einstein …

This book is the revised English edition of the Japanese book Introduction to Quantum
Information Theory, which systematically describes quantum information theory and was …

Quantum entanglement is at the heart of many tasks in quantum information. Apart from
simple cases (low dimensions, few particles, pure states), however, the mathematical …

Several well-established geometric and topological methods underscore the mathematical
treatment of the subject, emphasizing a coherent perspective at a rather sophisticated level …

An introductory textbook for advanced students of physics, chemistry and computer science,
covering an area of physics that has lately witnessed rapid expansion. The topics treated …

We consider the problem of maximizing a homogeneous polynomial on the unit sphere and
its hierarchy of sum-of-squares relaxations. Exploiting the polynomial kernel technique, we …