Symmetry and Quantum Information

Course manual 2017/2018

Course content

This course gives an introduction to quantum information theory. We use symmetries as a guiding principle and toolbox to study the fundamental features of quantum mechanics and their exploitation for information processing tasks.

Topics that will be treated: Basic formalism of quantum information theory, including partial traces, generalized measurements, quantum channels, and entanglement. Basic techniques in representation theory, such as Schur’s lemma and Schur-Weyl duality between the unitary and symmetric groups. How to model and compare classical and quantum correlations. How to exploit permutation symmetry to quantify the monogamy of quantum entanglement and securely distribute a secret key. How to use Schur-Weyl duality to study quantum information in the limit of many copies and construct universal quantum protocols; applications include compressing quantum data, estimating unknown quantum states, and transforming and distilling quantum entanglement.

This course will complement Ronald de Wolf’s course on Quantum Computing. Students interested in writing a thesis in quantum information theory are encouraged to follow both courses.

Study materials

Course homepage: https://staff.fnwi.uva.nl/m.walter/qit18/

Lecture notes will be offered on the course homepage on a weekly basis and may include pointers to supplementary reading material.

Background literature on quantum information theory:

• Nielsen and Chuang, Quantum Computation and Quantum Information
• Watrous, The Theory of Quantum Information
• Brandao, Christandl, Harrow, and Walter, The Mathematics of Entanglement

Background literature on representation theory:

• Fulton and Harris, Representation Theory: A First Course

Objectives

After successful completion of the course, students can

• use the basic mathematical formalism of quantum information theory;
• explain basic concepts and results of group representation theory;
• explain key objectives of quantum information theory and their motivation;
• model these objectives as mathematical problems and identify symmetries;
• apply representation theory to solve these problems.

Teaching methods

Lectures and homework.

Learning activities

Attendance

The programme does not have requirements concerning attendance (OER-B).

Assessment

There will be one problem set per week, posted on the course homepage by Monday, and you should submit your completed assignment before the Tuesday lecture the week after (either in class or by email).

Assignments will be accepted late only if you have extenuating circumstances (such as sickness or family emergency) and provided you confirm with the lecturer before the deadline.

Your lowest score on the problem sets will be ignored (this includes any problem set you did not submit).

Assignments

Collaboration on the problem sets is welcome and encouraged, but you must write up your solutions yourself. Please follow the regulations at www.uva.nl/plagiarism.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.uva.nl/plagiarism

Course structure

Timetable

The schedule for this course is published on DataNose.

Contact information

Coordinator

• dr. Michael Walter