Quantum correlations: Schrodinger's steering in lossy conditions; Heisenberg's limit to laser coherence.

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Wiseman, Howard M

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Saadatmand, Seyed N

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2021-06-16
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Abstract

Quantum correlations are a fundamental resource for technologies arising out of quantum information science. This thesis contains a body of work consisting of published and unpublished papers, which document theoretical developments in two active topics within this field - Einstein-Podolsky-Rosen (EPR) steering, and optical laser coherence. While these two topics might seem unrelated at first glance, all results contained within this work fundamentally arise from exploring the correlations between nonlocal quantum systems of low dimension. As such, this thesis is composed of two parts. The first is dedicated to studies of EPR steering, where one observer can appear to remotely steer (in the terminology of Schrodinger) the state of a distant party into different ensembles of quantum states. A number of novel results are presented which address the fundamental problem of determining both steerability and non-steerability of bipartite quantum states. Motivated by experiments aiming to demonstrate one-way steering, we begin by deriving a condition that can be applied to any two-qubit state, which is sufficient to determine if it is non-steerable when passed through a channel with a given amount of loss. This result is further expanded in the context of a new experiment, and applied to tomographically reconstructed two-qubit states which demonstrate one-way EPR steering in this rigorous way for the first time. Next, we develop a different idea for proving non-steerability of two-qubit entangled states, based on the idea of allowing the steering party to perform deterministic local quantum operations prior to measuring. Finally, we turn to the general issue of certifying steerability while closing the detection loophole, which has been previously closed in a number of experiments by violating specific loss-tolerant steering inequalities. Introducing a semi-definite programming formulation of the problem, we exploit the symmetry of a class of quantum states which naturally arise in quantum networks (the so-called inept states), to efficiently calculate the amount of loss they can tolerate while maintaining steerability. The collection of results in this first part are expected to be useful, especially as the field moves toward applications in networks where qubit loss becomes a limiting factor. The second part of this thesis concerns a defining property of a laser beam-optical coherence. This can be quantified by a dimensionless number, C, which can be roughly understood as the mean number of photons emitted into the beam with the same phase. While the fundamental theory of practical laser systems was developed in the 1950's and 60's, the ultimate quantum limits to the coherence of the beams a laser can produce has not been previously studied. In terms of the mean number of excitations stored inside the laser cavity, μ, it was previously thought that C = ø(μ2). Here, under some natural assumptions we show analytically that the ultimate limit permitted by quantum theory, or the Heisenberg limit, is quadratically better; C = O(μ4). Moreover, by treating the beam produced by a laser cavity as an infinite chain of entangled qubits, we use state-of-the-art matrix product state methods to numerically find a model of laser dynamics which attains this new ultimate limit. That is, C = ø(μ4). Finally, we present a system constructed with technology already existing in the field of circuit quantum electrodynamics, and use techniques from quantum control to prove that a coherent train of pulses attaining this limit can be created. The results presented in this part are a prescription for engineering a laser system operating at the best possible limit.

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Thesis (PhD Doctorate)

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Doctor of Philosophy (PhD)

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School of Environment and Sc

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The author owns the copyright in this thesis, unless stated otherwise.

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Quantum correlations

Einstein-Podolsky-Rosen steering

optical laser coherence

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