Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1604.01790

The Mathematics of Entanglement

Fernando G. S. L. Brandão, Matthias Christandl, Aram W. Harrow, Michael Walter

Published Apr 6, 2016• 11 citations
arXivHTMLPDF

Abstract

These notes are from a series of lectures given at the Universidad de Los Andes in Bogotá, Colombia on some topics of current interest in quantum information. While they aim to be self-contained, they are necessarily incomplete and idiosyncratic in their coverage. For a more thorough introduction to the subject, we recommend one of the textbooks by Nielsen and Chuang or by Wilde, or the lecture notes of Mermin, Preskill or Watrous. Our notes by contrast are meant to be a relatively rapid introduction into some more contemporary topics in this fast-moving field. They are meant to be accessible to advanced undergraduates or starting graduate students.

DOI
10.48550/arxiv.1604.01790

Related papers

Information and entanglement measures in quantum systems with applications to atomic physics

Daniel Manzano

Tesis Univ. Granada. Departamento de Fisica Atomica, Molecular y Nuclear. Leida el 12 de abril de 2010

•Apr 13, 2011•0 citations

A Quantum Approach to Condensed Matter Physics

Philip L. Taylor, Olle Heinonen

This textbook is an accessible introduction to the theory underlying the many fascinating properties of solids. Assuming only an elementary knowledge of quantum mechanics, it describes the methods by which one can perform calculations and make predictions of some of the many complex phenomena that occur in solids and quantum liquids. The emphasis is on reaching important results by direct and intuitive methods, and avoiding unnecessary mathematical complexity. Designed as a self-contained text that starts at an elementary level and proceeds to more advanced topics, this book is aimed primarily at advanced undergraduate and graduate students in physics, materials science, and electrical engineering. Problem sets are included at the end of each chapter, with solutions available to lecturers. The coverage of some of fascinating developments in condensed matter physics will also appeal to experienced scientists in industry and academia working on electrical properties of materials.

Cambridge University Press eBooks•Feb 28, 2002•85 citations

Complete hierarchies of efficient approximations to problems in entanglement theory (14 pages)

Jens Eisert, P. Hyllus

Physical Review A•Jan 1, 2004•0 citations

Lecture Notes on Quantum Many-Body Theory: A Pedagogical Introduction

Tafuri, Fabrizio, C. A. Perroni, G. De Filippis

In these notes, we present a rigorous and self-contained introduction to the fundamental concepts and methods of quantum many-body theory. The text is designed to provide a solid theoretical foundation for the study of interacting quantum systems, combining clarity with mathematical precision. Core topics are developed systematically, with detailed derivations and comprehensive proofs that aim to make the material accessible to graduate students and beginning PhD students. Special attention is given to formal consistency and pedagogical structure, so as to guide the reader through both the conceptual and technical aspects of the subject. This work is intended as a reliable starting point for further exploration and research in modern quantum many-body physics.

arXiv:2507.09229•Jul 12, 2025•0 citations

ON CLASSIFICATION OF QUANTUM ENTANGLED STATES (Mathematical Aspects of Quantum Information and Quantum Chaos)

V. P. Belavkin, Masanori Ohya

•Apr 1, 2000•0 citations

Measuring Wigner functions of quantum states of light in the undergraduate lab

Juan Rafael Álvarez, Andres Martinez, Alejandra Valencia

We present an educational activity for measuring Wigner distribution functions of quantum states of light in the undergraduate laboratory. The activity was implemented by undergraduate students in different courses of the undergraduate curriculum, and the resulting activity was tested by different students of an introductory Quantum Optics course at the Universidad de los Andes in Bogotá, Colombia. The activity consists of a two-hour laboratory practice where students work in a pre-aligned experimental setup and then use an open-access, custom made computational graphical user interface that enables the reconstruction of the Wigner distribution function. Since the testing of the activity coincided with the COVID-19 pandemic, the possibility of analyzing simulated data was included in the computational user interface. The activity is now running for in-person classes and its virtual feature is now valuable for the implementation of distance learning of Quantum Optics.

Education and Training in Optics and Photonics•Jun 28, 2023•1 citation
These notes are from a series of lectures given at the Universidad de Los Andes in Bogotá, Colombia on some topics of current interest in quantum information. While they aim to be self-contained, they are necessarily incomplete and idiosyncratic in their coverage. For a more thorough introduction to the subject, we recommend one of the textbooks by Nielsen and Chuang or by Wilde, or the lecture notes of Mermin, Preskill or Watrous. Our notes by contrast are meant to be a relatively rapid introduction into some more contemporary topics in this fast-moving field. They are meant to be accessible to advanced undergraduates or starting graduate students.
This textbook is an accessible introduction to the theory underlying the many fascinating properties of solids. Assuming only an elementary knowledge of quantum mechanics, it describes the methods by which one can perform calculations and make predictions of some of the many complex phenomena that occur in solids and quantum liquids. The emphasis is on reaching important results by direct and intuitive methods, and avoiding unnecessary mathematical complexity. Designed as a self-contained text that starts at an elementary level and proceeds to more advanced topics, this book is aimed primarily at advanced undergraduate and graduate students in physics, materials science, and electrical engineering. Problem sets are included at the end of each chapter, with solutions available to lecturers. The coverage of some of fascinating developments in condensed matter physics will also appeal to experienced scientists in industry and academia working on electrical properties of materials.
In these notes, we present a rigorous and self-contained introduction to the fundamental concepts and methods of quantum many-body theory. The text is designed to provide a solid theoretical foundation for the study of interacting quantum systems, combining clarity with mathematical precision. Core topics are developed systematically, with detailed derivations and comprehensive proofs that aim to make the material accessible to graduate students and beginning PhD students. Special attention is given to formal consistency and pedagogical structure, so as to guide the reader through both the conceptual and technical aspects of the subject. This work is intended as a reliable starting point for further exploration and research in modern quantum many-body physics.
We present an educational activity for measuring Wigner distribution functions of quantum states of light in the undergraduate laboratory. The activity was implemented by undergraduate students in different courses of the undergraduate curriculum, and the resulting activity was tested by different students of an introductory Quantum Optics course at the Universidad de los Andes in Bogotá, Colombia. The activity consists of a two-hour laboratory practice where students work in a pre-aligned experimental setup and then use an open-access, custom made computational graphical user interface that enables the reconstruction of the Wigner distribution function. Since the testing of the activity coincided with the COVID-19 pandemic, the possibility of analyzing simulated data was included in the computational user interface. The activity is now running for in-person classes and its virtual feature is now valuable for the implementation of distance learning of Quantum Optics.