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Quantum Information Theory (MATH M5600)

Academic Year:

Contents of this document:

Administrative Information

  1. Unit number and title: MATH M5600 Quantum Information Theory
  2. Level: M/7
  3. Credit point value: 10 credit points
  4. Year: 12/13
  5. First Given in this form: 2005/2006
  6. Unit Organiser: Noah Linden
  7. Lecturer: Prof N Linden and Dr A Short
  8. Teaching block: 2
  9. Prerequisites: A-Level Mathematics and one of: First year core units (MATH11006 Analysis 1, MATH 11007 Calculus 1, MATH 11005 Linear Algebra & Geometry), Introduction to Software Engineering (COMS 12100) or 1st year Physics units.

Unit 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.

General Description of the Unit

In the past fifteen 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 information 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 computation.

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.

Teaching Methods

Lectures, problem sheets.

Learning Objectives

At the end of the unit the student should:

  • Understand the concept of the qubit as the fundamental unit of quantum information
  • Be familiar with the ideas of quantum entanglement and non-locality and understand examples of their use and characterisation.
  • Understand examples of quantum information processing, including quantum teleportation

Assessment Methods

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.

Award of Credit Points

Credit points are gained by:

  • either passing the unit (i.e. gaining a mark of 50 or over),
  • or getting an examination mark of 30 or over and also handing in satisfactory attempts at half of the homework assignments.

Transferable Skills

The ability to assimilate and synthesize material from a wide variety of areas of science.

Texts

  • J. Preskill, Lecture notes, www.theory.caltech.edu/people/preskill 
  • M. Nielsen & I. Chuang, Quantum Computation and Quantum Information Theory, Cambridge University Press, 2000.
  • R.P. Feynman, Feynman Lectures on Computation, Addison Wesley 1996.

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
  • The concept of quantum information
  • No-cloning of quantum information
  • Measurement: outcomes correspond to eigenspaces; degenerate measurements
  • Multi-party states - tensor products; comparison to multiple classical systems
  • Entanglement
  • Classical bits; comparison of qubits to bits
  • Examples of multi-party quantum states including EPR
  • Local operations, local measurements
  • Quantum Dense Coding
  • Quantum Teleportation
[7 lectures]
Topics chosen from
  • State estimation
  • Density matrices, traces over subsystems: von-Neumann entropy
  • Decoherence and entanglement
  • Quantum Cryptography
  • Non-locality/Bell inequalities
  • Quantification of entanglement of pure states
  • Concentration of entanglement
  • Classical information: Shannon information
  • Quantum Computation
  • Quantum algorithms
[8 lectures]