  In parameter estimation, nuisance parameters refer to parameters that are not
of interest but nevertheless affect the precision of estimating other
parameters of interest. For instance, the strength of noises in a probe can be
regarded as a nuisance parameter. Despite its long history in classical
statistics, the nuisance parameter problem in quantum estimation remains
largely unexplored. The goal of this article is to provide a systematic review
of quantum estimation in the presence of nuisance parameters, and to supply
those who work in quantum tomography and quantum metrology with tools to tackle
relevant problems. After an introduction to the nuisance parameter and quantum
estimation theory, we explicitly formulate the problem of quantum state
estimation with nuisance parameters. We extend quantum Cramer-Rao bounds to the
nuisance parameter case and provide a parameter orthogonalization tool to
separate the nuisance parameters from the parameters of interest. In
particular, we put more focus on the case of one-parameter estimation in the
presence of nuisance parameters, as it is most frequently encountered in
practice.
