Quantum Information Theory

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.

Unit description

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.  It is a pre-requisite for Quantum Computation (MATHM0023).

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

Transferable skills

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

Syllabus

7 lectures:

  • 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

8 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

Reading and References

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

Unit code: MATHM5610
Level of study: M/7
Credit points: 10
Teaching block (weeks): 1 (1-6)
Lecturer: Professor Noah Linden

Pre-requisites

Analysis 1A, Analysis 1B, Calculus 1, Linear Algebra and Geometry or COMS12100 Introduction to Software Engineering or 1st year Physics units.

Co-requisites

None

Methods of teaching

Lectures, problem sheets.

Methods of Assessment 

The pass mark for this unit is 50.

The final mark is calculated as follows:

  • 100% from a 1 hour 30 minute exam in January

NOTE: Calculators are not allowed in the examination.

For information resit arrangements, please see the re-sit page on the intranet.

Please use these links for further information on relative weighting and marking criteria.

Further exam information can be found on the Maths Intranet.

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