ETD Collection

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    Manipulating & measuring quantum ghosts & randomness
    (2021) Bornman, Nicholas
    Despite having been around for roughly 85 years, quantum mechanics continues to produce many surprising results. Furthermore, although theoretical work aiming to fully complete quantum mechanics is still ongoing, the form typically employed in quantum information and quantum computing studies can be axiomatised by four succinct postulates. In this work we will discuss, in detail, four interesting quantum photonics and quantum information experiments which can neatly be divided into two groups: quantum ghost imaging and quantum random number generation. The interplay between the four postulates underpinning contemporary quantum mechanics, and the experiments themselves, will also be touched on throughout this work. First, we present a novel four-way quantum ghost imaging setup which employs entanglement swapping to create correlations between initially completely independent down-converted biphoton states. The projection and measurement techniques used give rise to an anti-symmetric biphoton state (in contrast with the symmetric states normally used in quantum ghost imaging). This, in turn, results in a surprising ‘contrast-reversed’ ghost image with respect to the original object; the symmetric case would give rise to an ordinary ghost image. Such considerations of state symmetry may prove important in future higher-dimensional imaging and communication protocols which incorporate entanglement swapping (which is a key component of a future quantum network). Second, we investigate the connection between ghost imaging and state symmetry further by using a two-way ghost imaging experiment which is modified to tailor the symmetry of the down-converted state. In this case, when postselecting on antisymmetric subspaces, the reconstructed ghost image turns out to be a juxtaposed version of the original object, rotated both clockwise and counterclockwise. This again emphasises the importance a state’s symmetry has on the observed physics. Third, although quantum mechanics has been an extremely successful theory, it is fundamentally incomplete. We therefore explore the potential of using quantum field theory, which is a more complete set of ideas, to explain quantum ghost imag- x ing specifically and the measurement/detection process in quantum photonics more generally. We find that the so-called Unruh-DeWitt detector model is successful in explaining quantum ghost imaging when one draws an analogy between the pixels comprising the original object plus the pixels comprising the measurement device, and two arrays of Unruh-DeWitt detectors. This different approach may be a useful first step in considering quantum imaging in non-inertial reference frames and the nature of entanglement of down-converted states in nontrivial gravitational backgrounds, for example. Finally, a key feature of quantum mechanics is the inherent indeterminacy built into the formalism, by way of the postulates. We present work whereby this uncertainty is exploited to demonstrate the generation of true higher-dimensional random numbers from the orbital angular momentum degree of freedom of down-converted biphoton states. Digital spatial light modulators are used to tailor the probability distribution of the state, allowing us to mitigate bias and imperfections in the experimental setup. With these techniques, we are able to generate more than one bit of truly random information from each orbital angular momentum detection event. Entropy and randomness are increasingly important both fundamentally and commercially, and hence such proof of principle studies are important.
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    Exact global symmetry generators for restricted Schur polynomials
    (2016) Bornman, Nicholas
    The six scalar fields in N = 4 super Yang-Mills theory enjoy a global SO(6) symmetry, and large N but non-planar limits of this theory are well-described by adopting a group representation approach. Studies have shown that the one-loop dilatation operator is highly determined by the action of the su(2)=su(3) subalgebras on restricted Schur polynomials. These actions involve the traces of products of projection operators. In this dissertation, exact analytical formulae for these traces are found which in turn are used to find the exact action of these algebras on restricted Schur polynomials. The potential of the su(2) algebra to determine the one-loop dilatation operator is also explored. This is done by exploiting necessary symmetry conditions and moving to a continuum limit in order to derive a number of partial differential equations which determine the dilatation operator. The ultimate goal of this work is to provide tools to find the exact one-loop dilatation operator in the non-planar limit.