  The reliable characterization of quantum states as well as any potential
noise in various quantum systems is crucial for advancing quantum technologies.
In this work we propose the concept of corrupted sensing quantum state
tomography which enables the simultaneous reconstruction of quantum states and
structured noise with the aid of simple Pauli measurements only. Without
additional prior information, we investigate the reliability and robustness of
the framework. The power of our algorithm is demonstrated by assuming Gaussian
and Poisson sparse noise for low-rank state tomography. In particular, our
approach is able to achieve a high quality of the recovery with incomplete sets
of measurements and is also suitable for performance improvement of large
quantum systems. It is envisaged that the techniques can become a practical
tool to greatly reduce the cost and computational effort for quantum tomography
in noisy quantum systems.
