| Unit name | Quantum Information Theory |
|---|---|
| Unit code | MATHM5610 |
| Credit points | 10 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Professor. Linden |
| Open unit status | Not open |
| Pre-requisites |
A-Level Mathematics and one of: Core Mathematics (MATH1102/3), Introduction to Software Engineering (COMS12100) or 1st year Physics units. |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
In the past ten years the new subject of quantum information theory has emerged which both offers fundamentally new methods of processing information and also suggests deep links between the well-established disciplines of quantum theory and information theory and computer science. The unit aims to give a self-contained introduction to quantum inofrmation theory accessible to students with backgrounds in mathematics and physics; it is also suitable for mathematically inclined students from computer science. The course will begin with a brief overview of the relevant background from quantum mechanics and information theory. The main theme of the course, quantum information and entanglement, then follows. The subject will be illustrated by some of the remarkable recent ideas including quantum teleportation and quantum cryptography.
Aims
The course aims to give a self-contained introduction to quantum information theory accessible to students with backgrounds in mathematics, physics or computer science. Additionally, in conjunction with other units, it should provide suitably able and inclined students with the necessary background for further study and research at the postgraduate level.
Syllabus
The space of quantum states, Cn, as a linear space Ket notation The space of qubits as an example Inner product Operators, Hermitian, Unitary, Projection No-cloning of quantum information Measurement: outcomes correspond to eigenspaces; degenerate measurements Multi-party states - tensor products; comparison to multiple classical systems Classical bits; comparison of qubits to bits Examples of multi-party quantum states including EPR; mention of entanglement Local operations, local measurements Density matrices, traces over subsystems: von-Neumann entropy Quantum Dense Coding Quantum Teleportation [8 lectures] Topics chosen from
State estimation Decoherence and entanglement Quantum Cryptography Non-locality/Bell inequalities Quantification of entanglement of pure states Concentration of entanglement Classical information: Shannon information The concept of quantum information Quantum algorithms
Relation to Other Units
The unit aims to be self-contained: it does not require knowledge of any particular course in previous years, nor is it a pre-requisite for other courses.
At the end of the unit the student should:
Transferable Skills:
The ability to assimilate and synthesize material from a wide variety of areas of science.
Lectures, problem sheets.
The final assessment mark for Quantum Information Theory is calculated from a 2-hour written examination in May/June consisting of THREE questions. A candidate's best TWO answers will be used for assessment. Calculators are NOT permitted in this examination.
