Classical and quantum entanglement: applications to quantum communication with structured photons
Ndagano, Bienvenu Irenge
Generating, manipulating and sharing quantum states with maximal levels of entanglement are crucial steps when implementing quantum processes such as quantum key distribution, quantum teleportation or quantum computation. In this quest, realising entanglement in di erent degrees of freedom has opened avenues beyond the two-level quantum bit (qubit). Spatial modes, particularly those carrying orbital angular momentum (OAM), allow one to exploit the spatial properties of photons to realise highdimensional entanglement. This is owing to their larger Hilbert space that allows one to pack more information onto photons. Interestingly, the exploration of entanglement in many degrees of freedom has led to a topical debate around the quantum nature of entanglement itself. Non-separability is a fundamental property of quantum entangled states. However it is not unique to quantum systems; classical states of light can exhibit non-separability in their degrees of freedom which, can then be said to be entangled. Due to the local nature of this entanglement, these classical correlations have come to be known as classical entanglement. Entanglement correlations are, however, fragile and susceptible to decay under the in fluence of external factors such as atmospheric turbulence or imperfections in optical bres. Here we provide a toolbox to characterise entanglement dynamics, mitigate photon loss, and compensate for errors. On the characterisation aspect, we demonstrate for the rst time, the equivalence of quantum and classical entanglement in a one-sided turbulent channel. By performing a state tomography of an entangled two-photon state and a classically entangled beam postperturbation, we show that the decay of entanglement for both systems is identical. This opens the possibility for real-time measurement of the channel operator and mitigation of errors on the quantum state, using bright laser sources. This is complemented by a number of schemes to mitigate errors and losses incurred on the quantum state through the perturbing channel. (1) In a simulated quantum key distribution protocol, we demonstrate the e ect of mode separation on the robustness of the protocol: the larger the separation in state space, the more robust the link. (2) Turbulence causes intermodal scattering and results in photon loss during post-selection of a particular subspace. We show that information scattered in a larger state space as a result of turbulence can be recovered by post-selecting higher-dimensional spaces. Using a theoretical model based on experimental observations, we provide bounds within which the scheme is e ective, as well as an estimation of the e ciency of photon recovery. (3) We make use of the channel characterisation with bright classical light to implement a Procrustean ltering on entangled photons; that is, we perform local operations on the quantum state to increase its degree of entanglement. Unlike previous schemes, our ltering only requires the local operations to be performed on a single party in the entangled pair, as opposed to both. While this requires prior knowledge of the perturbed state, the next scheme does not. (4) We demonstrate the concentration of entanglement by Hong-Ou-Mandel interference. We show that singlet Bell states can be distilled from an ensemble of pure states with near-zero levels of entanglement. The robustness of the ltering is such that the delities of the distilled states remain constant over a large range of turbulence conditions. (5) Lastly, we address the issue of photon loss arising from the nature of the detector in the context of quantum key distribution. We present a novel scheme to deterministically measure single photons in a high-dimensional space of classically entangled vector vortex modes. Our scheme, unlike common lter-based ones, does not su er from dimension-dependent losses, allowing the sorting of vector vortex modes with, in principle, unit e ciency.
A thesis submitted in ful lment of the requirements for the degree of Doctor of Philosophy in the School of Physics 13 March 2019