Engineering robust photonic quantum states for quantum communication and information
Nape, Isaac Mphele
Quantum communication and information processing with photons achieves the overarching goals of transferring, encrypting, and processing digital information using machinery provided by fundamental physics principles that are established in quantum mechanics. In the last decade, the field has matured rapidly, from being the bedrock of simple demonstrations of quantum key distribution protocols with typical polarisation qubits that have two dimensional (𝑑 = 2) alphabets to now overseeing accelerated developments with high dimensional encoding using alternative photonic degrees of freedom (DOFs) that span larger Hilbert spaces of dimensions 𝑑 > 2. Excitingly, the transverse spatial DOF of light offers an infinite encoding alphabet. While spatial modes may be transported over most propagation media, i.e. free-space, optical fiber and underwater channels, they are easily perturbed by various noise mechanisms, e.g., rapidly varying refractive index profiles, diffraction, mode dependent loss, inhibiting their performance in practical applications. Most potential approaches for undoing these deleterious effects require full knowledge of the channel dynamics or the state evolution. In relation to the latter we can highlight the following challenges for transverse spatial mode encoding that are prevalent in the field: i) the internal modal scattering due to the perturbations from a quantum channel for spatial modes can be difficult to predict; ii) and when possible, accurate characterisation methods are required before the effects of the channel can be undone; iii) in higher dimensions, characterising quantum states become increasing difficult due to the quadratic scaling of the number of measurements with respect to the dimensions. In this Thesis we tackle these issues by engineering techniques for creating, controlling and characterising photons that are subject to a diverse range of perturbative ii channels. For channels, that cause diffraction induced losses, we tailor non-diffracting higher dimensional vectorial photon fields, that have coupled polarisation and azimuthal spatial components, modulated with self-healing radial profiles. We show that these fields can be used to transmit secure quantum information in the presence of disturbances. We overcome the scattering effects of optical media with spatially varying refractive index, by invoking channel state duality and the invariance of nonseparable states to unitary channels, but in locally entangled vectorial photon fields. This approach enables us to devise a procedure for undoing the effects of a channel in order to preserve information encoded in spatial modes. This method advances the use of so called classical entanglement in quantum and classical optics. Next, we develop a technique that manipulates heterogeneous channels to deliver multiple hybrid non-locally entangled states using a single mode fiber channel. The nonlocal hybrid entanglement between the polarisation and high dimensional spatial modes of two spatially separated photons is used as main resource. Lastly, we develop a novel technique for characterising high dimensional quantum states that are affected by white noise. The procedure involves the use of conditional measurements that return crucial information about the underlying states’ occupied dimensions and purity. We demonstrate the feasibility and adaptability of our approach using photons that have nonlocal entanglement between their transverse spatial modes of orbital angular momentum, and separately using the pixel position basis.
A thesis submitted in fulfilment of the academic requirements for the degree of Doctor of Philosophy to the Faculty of Science, School of Physics, University of the Witwatersrand, Johannesburg, 2022