Shackerley-Bennett, Uther;
(2018)
The control of Gaussian quantum states.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
The rise of quantum technology has put control at the centre of advancements in quantum mechanics. The union of quantum mechanics with mathematical control theory is a meeting that is leading to a much deeper insight into our interaction with the bizarre properties of quantum theory. Often, the study of discrete variable systems is the focus for making this union. Here, we look at how control theory may be applied to the continuous variable theory of Gaussian states. Special emphasis is given to control of the covariance matrix of these states, as it is here that we find the entanglement and entropic properties of the state. We begin by exploring some initial results for the geometry of Gaussian states, revealing different manifold structures dependent on symplectic eigenvalue degeneracy. In this geometrical setting a proposal for an extension of Williamson's theorem is put forward and partially completed. It is often interesting to look at restricted sets of Hamiltonians and ask what transformations can be performed with concatenations of their corresponding unitaries. Controllable systems are those for which the entire group of interest is possible to enact. We explore an uncontrollable system in a single mode and give a physical analysis as to why it behaves this way. This leads to ideas to move forwards for a necessary and sufficient condition for control on the symplectic group that has been conjectured since 1972. Later, we transfer to the question of open dynamics. We focus on a particular and ubiquitous channel known as 'lossy' or 'the attenuation channel'. An equation is derived describing the evolution for the symplectic invariants of a Gaussian state undergoing such dynamics. The equation of the former chapter is used to explore the evolution of entropy and entanglement. Optimal protocols are developed for the manipulation of these properties undergoing lossy dynamics.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | The control of Gaussian quantum states |
| Event: | UCL |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10040959 |
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