# Geometry of quantum noise

 Title: Geometry of quantum noise Author: Dixit, Kuldeep Narayan Abstract: 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 . URI: http : / /hdl .handle .net /2152 /ETD -UT -2010 -05 -771 Date: 2010-09-16

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