  A quantum channel is a mapping which sends density matrices to density
matrices. The estimation of quantum channels is of great importance to the
field of quantum information. In this thesis two topics related to estimation
of quantum channels are investigated. The first of these is the upper bound of
Sarovar and Milburn (2006) on the Fisher information obtainable by measuring
the output of a channel. Two questions raised by Sarovar and Milburn about
their bound are answered. A Riemannian metric on the space of quantum states is
introduced, related to the construction of the Sarovar and Milburn bound. Its
properties are characterized. The second topic investigated is the estimation
of unitary channels. The situation is considered in which an experimenter has
several non-identical unitary channels that have the same parameter. It is
shown that it is possible to improve estimation using the channels together,
analogous to the case of identical unitary channels. Also, a new method of
phase estimation is given based on a method sketched by Kitaev (1996). Unlike
other phase estimation procedures which perform similarly, this procedure
requires only very basic experimental resources.
