Universal framework for simultaneous tomography of quantum states and measurement noise.

We present a general denoising algorithm for performing quantum tomography in the presence of detector noise. Our method is based on analyzing the properties of the linear operator space induced by unitary gate operations and given any quantum system with a noisy measurement apparatus, our method can output the quantum state and the noise matrix of the detector up to a single gauge degree of freedom. We show that this gauge degree of freedom is unavoidable in the general case and show how to eliminate this degeneracy and fix the gauge for several interesting special cases including pure quantum states and block independent detector noise. Our framework can readily use prior information available about the system to systematically reduce the number of observations and measurements required for state and noise detection. Our method effectively generalizes many previous approaches to the problem and many of the methods in the literature that require an invertible noise matrix or specific probe states can be obtained as special cases.