Środowiskowe Seminarium z Informacji i Technologii Kwantowych

For the last 20 years, the research on quantum information processing is experiencing a rapid growthand holds great promise for revolutionary new technology. In the development of these quantumtechnologies efficient and flexibel methods for extracting information about a quantum state frommeasurements are required. One important task is to fully determine a quantum state from the measured data with only mild structure assumptions on the state. This is the problem of quantum statetomography.Using a signal processing paradigm called compressed sensing, quantum tomography schemes for lowrank states were developed that are resource-optimal. But to date compressed sensing schemes forquantum state tomography lack robustness against imperfection of the measurement devices. For thisreason, experimental setups performing these schemes need to have measurements devices that arecalibrated to a high precision. In this work we develop the framework of blind calibration tomography which allows for incomplete knowledge of the measurement device during the tomography of aquantum state. It simultaneously determines both the device calibration and the quantum state withminimal resources and efficient classical post-processing.Building on recent techniques from the field of compressed sensing, we derive algorithmic strategiesfor blind calibration tomography and provide analytical performance guarantees. We further demonstrate their performance in numerical simulations.