ERROR REGIONS FOR SELF-CALIBRATING QUANTUM TOMOGRAPHY AND SAMPLING OF QUANTUM CHANNELS

Abstract

The first part of this thesis studies the problem of proper error regions for self-calibrating quantum tomography. Self-calibrating quantum state tomography aims at reconstructing the unknown quantum state and certain properties of the apparatus from the same data. Since the estimation is done from the same data, the proper approach to quantify the uncertainty is to report joint state-apparatus error regions. We explain how this can be done naturally within the framework of optimal error regions and demonstrate our method with two examples. The second part of this thesis focuses on random sampling of quantum channels. Due to the Choi-Jamiołkowski isomorphism, the Hamiltonian Monte Carlo method which was previously applied to state sampling problems can be adapted to sampling of quantum channels. Its implementation requires a parameterization of the channel space with no constraints and no superfluous parameters. We construct such a parameterization and demonstrate its use in three applications.