Study-Unit Description

Study-Unit Description


TITLE Modern Quantum Theory

LEVEL 03 - Years 2, 3, 4 in Modular Undergraduate Course



DESCRIPTION Information must be fundamentally stored and processed in a physical media. When this media approaches the scales of single particles, quantum mechanical effects persist and new - often described as counter intuitive - modes of operation become possible.

This is the setting for the modern account of quantum theory and studying this quantum information implicitly represented in naturally occurring quantum systems and engineering quantum systems - particularly quantum optical systems - to preserve quantum information is a topic of tantamount contemporary interest.

The theory is used to describe a host of physical phenomena, as well an engineered devices used for quantum secure communication and quantum enhanced sensing. This study-unit builds on past units in statistical physics, solid-state physics and quantum theory, bringing these topics together and building a tool set to analyze several naturally occurring and engineered systems where quantum effects dominate.

Study-unit Aims:

This study-unit aims to endow final-year students with a deeper knowledge of techniques and ideas related to modern quantum information theory. This unit will first undertake a short survey of various quantum effects and technologies that utilize them, with a particular focus on devices based on quantum optics. It will undertake of techniques to solve one-dimensional quantum systems, showing how key properties of such systems can be calculated. Following a discussion of quantum entropy and correlation measures, as well as their applications to quantum phenomena, the quantificiation of quantum effects in open and closed systems will be tackled. A description of time-reversal symmetry breaking in closed and open quantum systems will allow the discussion of topological states of matter.

Learning Outcomes:

1. Knowledge & Understanding
By the end of the study-unit the student will be able to:

- understand the various quantum effects which are being employed in a range of engineered devices;
- solve several 1D quantum systems and calculate relevant quantities of interest;
- apply entropy and correlation measures to describe properties of quantum systems;
- derive the von Neumann entropy and derive quantum thermal (Gibbs) states;
- describe symmetry breaking in quantum systems, Noether currents, time-symmetry and associated effects;
- use techniques found in quantum computation which are being employed in a new class of quantum enhanced sensors.

2. Skills
By the end of the study-unit the student will be able to:

- employ several techniques to exactly solve 1D quantum systems;
- apply entropy and correlation measures to various phenomena, including information encoding;
- work with and manipulate and understand several measures of information and entropy and to use these tools to quantify information in quantum and stochastic systems;
- determine when a quantum system exhibits symmetry breaking;
- determine conserved quantities of a quantum system;
- employ the basic quantum computer algorithm known as phase-estimation as a means to describe a new class of quantum enhanced sensors; understand the range of uses of these sensors.

Main Text/s and any supplementary readings:

- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press), 2010.
- J. K. Pachos, Introduction to Topological Quantum Computation (Cambridge University Press), 2012.

ADDITIONAL NOTES Pre-Requisite Study-unit: PHY2140


Assessment Component/s Assessment Due Resit Availability Weighting
Examination (2 Hours) SEM2 Yes 100%

LECTURER/S Tony John George Apollaro
Andre Xuereb

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It should be noted that all the information in the description above applies to study-units available during the academic year 2020/1. It may be subject to change in subsequent years.