Quantum tomography for high dimensional systems

Project description

Quantum Technology is a fast developing field which aims to harness quantum phenomena such as entanglement and superposition in a broad array of applications ranging from secure communication and faster computation to high precision metrology and imaging.

Building a successful quantum device relies on the ability to prepare quantum systems in specifically designed states, and to accurately manipulate and measure the different components of the device.

Since quantum measurements are intrinsically stochastic, statistical inference plays a key role, enabling the experimenter to interpret the measurement data and validate the functioning of the device.

An important component of the quantum engineering toolbox is quantum tomography: the estimation of unknown quantum states based on random outcomes of measurements performed on identically prepared quantum systems. Although many estimation methods have been explored theoretically and experimentally, there is currently a need for new techniques to deal with inference for high dimensional quantum states.

This PhD project aims to develop efficient methods for computing point estimators and confidence regions for multipartite quantum states. In particular we will be interested in statistical models which take into account prior information about the state, in the form of correlation structure, rank, or symmetry. The project involves both theoretical and computational work; prior knowledge of quantum mechanics is beneficial but is not an absolute requirement. The PhD student with work together with Dr Madalin Guta and Dr Theo Kypraios who have a leading expertise in statistical aspects of quantum theory and have developed a range of computational tools for quantum tomography, see [1,2,3,4]. The project builds on the group's prior work in the field and will benefit from contacts with external collaborations on both theoretical and practical aspects.