Open quantum systems refer to systems that are affected by
interaction with the environment. The effects of these unwanted
interactions, called \emph{quantum noise}, are studied using
dynamical maps. We study the geometry of these maps in this work.
We review the canonical representations of dynamical maps such as
reduced dynamics, $\mathcal{A}$ and $\mathcal{B}$ forms and
operator sum representation. We develop a framework for
simplifying the action of dynamical maps in terms of their action
on the coherence vector associated with the density matrix. We use
the framework to describe the geometry of depolarization,
dephasing and dissipation in the domain of complete positivity. We
give a geometric picture of how two-, three- and four-level
systems are affected by these common forms of quantum noises. We
show useful similarities between two- and four-level depolarizing
maps and give a generalization for $n$-qubits. We also derive
important results that restrict dephasing and dissipation. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/ETD-UT-2010-05-771 |
| Date | 16 September 2010 |
| Creators | Dixit, Kuldeep Narayan |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Type | thesis |
| Format | application/pdf |
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