Vectorization of quantum operations and its use

Alexei Gilchrist, Daniel R. Terno, Christopher J. Wood

Published 2009-11-13, updated 2011-08-18Version 2

We give a detailed exposition of the "vectorized" notation for dealing with quantum operations. This notation is used to highlight the relationships between representations of completely-positive dynamics. Vectorization considerably simplifies the analysis of different methods of quantum process tomography, and enables us to derive compact representation of the investigated quantum operations in terms of the resulting data.