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Unit information: Quantum Information Theory in 2023/24

Unit name Quantum Information Theory
Unit code MATHM0047
Credit points 20
Level of study M/7
Teaching block(s) Teaching Block 2 (weeks 13 - 24)
Unit director Professor. Linden
Open unit status Not open
Units you must take before you take this one (pre-requisite units)

None

Units you must take alongside this one (co-requisite units)

None

Units you may not take alongside this one

None

School/department School of Mathematics
Faculty Faculty of Science

Unit Information

This unit will only run in 2023/24. From 2024/25, only the Year 3 version MATH30031 will be available.

Why is this unit important?

Over the past few decades, 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.

How does this unit fit into your programme of study?

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.

Your learning on this unit

An overview of content

  • Mathematical tools for quantum mechanics (inc. Dirac notation)
  • The rules of quantum mechanics
  • Multi-party quantum systems
  • Key quantum information primitives: no-cloning, super-dense coding, teleportation
  • Introduction to quantum computing: Deutsch's and the Deutsch-Jozsa algorithm
  • Quantum cryptography
  • Density operators and reduced density operators
  • The Bloch sphere
  • Bell's theorem and quantum nonlocality

Topics selected from:

  • Additional structure of quantum mechanics (Generalised measurements, Von Neumann entropy, sub-additivity, mixed entangled states and separability, learning quantum states)
  • Further Applications (Quantum data compression, entanglement concentration, entanglement swapping)
  • Further aspects of nonlocality (GHZ paradox, Nonlocality beyond quantum mechanics (PR boxes), EPR steering)
  • Systems interacting with their environment (noise processes, thermalisation, noise as entanglement with the environment)

How will students, personally, be different as a result of the unit

At the end of the unit the students will have improved their logical thinking, learnt to synthesize ideas from different disciplines, and have increased the range and scope of their problem-solving techniques.

Learning Outcomes

At the end of the unit the student should:

  • Explain the concept of the qubit as the fundamental unit of quantum information.
  • Define the concepts of quantum entanglement and non-locality and describe examples of their use and characterisation.
  • Describe examples of quantum information processing, including quantum teleportation, dense coding and quantum cryptography
  • Explain what a density operator is, and use it to classify pure and mixed states; apply the density operator formalism to carry out calculations involving mixed states, and for identifying entanglement.

Transferable Skills

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

How you will learn

The unit will be taught through a combination of:

  • Asynchronous online materials, including narrated presentations and worked examples-guided
  • Asynchronous independent activities such as problem sheets and/or other exercises-
  • Synchronous weekly group problem/example classes, workshops and/or tutorials
  • Synchronous weekly office hours

How you will be assessed

Tasks which help you learn and prepare you for summative tasks (formative):

Weekly problem sheets

Tasks which count towards your unit mark (summative):

100% Timed, open-book examination

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

When assessment does not go to plan

The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).The Board of Examiners will take into account any exceptional circumstances and operates within the Regulations and Code of Practice for Taught Programmes.

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATHM0047).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the University Workload statement relating to this unit for more information.

Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates within the Regulations and Code of Practice for Taught Programmes.

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