  We formulate the accuracy of quantum measurement for a qubit system in terms
of a 3 by 3 matrix. This matrix, which we refer to as the accuracy matrix, can
be calculated from a positive operator-valued measure (POVM) corresponding to
the quantum measurement. Based on the accuracy matrix, we derive new trade-off
relations between the measurement accuracy of two or three noncommuting
observables of a qubit system. These trade-off relations offer a quantitative
information-theoretic representation of Bohr's principle of complementarity.
They can be interpreted as the uncertainty relations between measurement errors
in simultaneous measurements, and also as the trade-off relations between the
measurement error and back-action of measurement. A no-cloning inequality is
derived from the trade-off relations. Furthermore, our formulation and the
obtained results can be applied to analyze quantum state tomography. We also
show that the accuracy matrix is closely related to the maximum-likelihood
estimation and the Fisher information matrix for a finite number of samples;
the accuracy matrix tells us how accurately we can estimate the probability
distributions of observables of an unknown state by quantum measurement.
