Universal characterization of quantum optical devices: Theory and practice
The primary vision of my group’s research is implementing light as the principal physical medium for quantum information processing. Light is an ideal communication agent: because the energy of the photon is normally much higher than the average temperature of the environment, it can propagate many miles without losing the information it carries. Therefore, no matter what physical system will be the basis for future quantum computers, these computers will have to use photons to talk to each other. Furthermore, even if scientists fail to develop quantum computers in near future, quantum-optical information technology is still useful as a tool for confidential communication protocols whose security is guaranteed by fundamental laws of nature.
While the initial applications showed the promise of our approach, additional work is needed in order to make this procedure a universal standard for quantum device characterization. In particular, a robust algorithmic framework for the process reconstruction needs to be elaborated. We would like to generalize the maximum-likelihood algorithm for quantum state tomography  to estimate the process tensor and its uncertainties directly from the experimental data acquired in homodyne detection, removing the intermediate step of reconstructing for the “probe” coherent states. This algorithm will improve the stability of the reconstruction and guarantee a physically consistent result.
We also need to improve our understanding of many practical issues involving our process tomography, such as better understanding the sources of error in our procedure and developing a reliable technique for estimating this error and determine the set of coherent states for which the measurements need to be performed in order to achieve a required level of precision in process reconstruction.
If the student prefers theory, he or she can, for example, elaborate the direct algorithm of process reconstruction from the experimental data. On the experimental side, the student can join an experiment on process tomography of the creation and annihilation operators.