  The accurate detection of small deviations in given density matrices is
important for quantum information processing. Here we propose a new method
based on the concept of data mining. We demonstrate that the proposed method
can more accurately detect small erroneous deviations in reconstructed density
matrices, which contain intrinsic fluctuations due to the limited number of
samples, than a naive method of checking the trace distance from the average of
the given density matrices. This method has the potential to be a key tool in
broad areas of physics where the detection of small deviations of quantum
states reconstructed using a limited number of samples are essential.
