Toolkit for high-dimensional quantum light

Abstract

The manipulation of light’s various degrees of freedom, known as structuring light, has become useful in the development of both classical and quantum technologies. Two-dimensional quantum states have been investigated optically for many years, but have a limited amount of information which can be encoded into them. In order to surpass this limitation, high-dimensional quantum states have also been studied using light in quantum optics experiments. High-dimensional quantum states al- low for large amounts of information to be encoded into the states and bi-photon quantum states present an added advantage of non-local measurements. However, high-dimensional bi-photon states impose challenges such as efficient generation and detection of the states. In this dissertation we explore a generation technique for high dimensional states as well efficient detection techniques and methods which can be employed to com- bat challenges which may arise. The high-dimensional degrees of freedom that will be used are orbital angular momentum and transverse spatial position. The cor- relations between a pair of entangled photons are exploited in order to perform measurements on a bi-photon high-dimensional quantum state. The theory and experimental implementation of characterisation techniques for high-dimensional quantum states are discussed such as OAM bandwidth measurements, Bell inequal- ity violations and reconstructing the information of a quantum state using quantum state tomography. Quantum ghost imaging is a quantum imaging technique that uses the transverse position correlations between the entangled photons. The theory and experimental implementation of ghost imaging using high-dimensional bi-photon position states is explored. The uncertainty principle between angular position and OAM is inves- tigated for a bi-photon quantum state and how a non-local induced OAM spread is limited by the spread in OAM of the initial quantum state produced from spon- taneous parametric down-conversion. A link between a quantum search algorithm (Grover’s algorithm) and quantum ghost imaging is investigated and similarities are drawn. The complexity of Grover’s algorithm is alleviated by leveraging high- dimensional bi-photon position states.