Classical and quantum entanglement: applications to quantum communication with structured photons
Date
2019
Authors
Ndagano, Bienvenu Irenge
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Abstract
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.
Description
A thesis submitted in ful lment of the requirements
for the degree of Doctor of Philosophy
in the School of Physics
13 March 2019