  In this paper, we analyze quantum-state estimation problems when some of the
parameters are of no interest to be estimated. In classical statistics, these
irrelevant parameters are called nuisance parameters and this problem is of
great importance in many practical applications of statistics. However, little
is known regarding the effects of nuisance parameters in quantum-state
estimation problems. The main contribution of this paper is first to formulate
the nuisance parameter problem for the quantum-state estimation theory, then to
propose a method of how to eliminate the nuisance parameters to obtain an
estimation error bound for the parameters of interest. We also develop useful
methods of dealing with the nuisance parameter problem in the quantum case and
reveal the significant difference from the classical case. In particular, we
clarify an intrinsic tradeoff relation to estimate the nuisance parameters and
parameters of interest. The general qubit model is examined in detail to
emphasize that we cannot ignore the effects of the nuisance parameters in
general. Several examples in qubit systems are worked out to illustrate our
findings.
