In this thesis we examine methods for measuring entanglement entropy in spin-1/2 Heisenberg systems using quantum Monte Carlo in the valence bond basis. We begin by presenting the quantum Monte Carlo techniques used in this research. We then use these techniques to directly compare the recently proposed valence bond entanglement entropy to the standard definition of entanglement entropy: the von Neumann entanglement entropy. We find that the valence bond entanglement entropy does not give a bound on the von Neumann entanglement entropy, and that it exhibits a multiplicative logarithmic correction to the area law that is not present in the scaling of the von Neumann entanglement entropy. We then present a method to measure higher orders of the generalized Renyi entanglement entropies using valence bond quantum Monte Carlo, and show results for the second Renyi entropy. We find the results converge to the exact results for one dimensional Heisenberg spin-1/2 chains, and see that the scaling of the second Renyi entropy follows an area law in the two dimensional Heisenberg ground state.

This thesis is the synthesis of theoretical and experimental works performed in the area of quantum foundations, particularly on quantum correlations and experimental tests of multiplicative Bell inequalities. First we begin with a comprehensive theoretical work performed on the foundations of quantum mechanics, focusing on the puzzling concepts of quantum entanglement, and hidden variable theories. Specifically, we present a broad overview of different classes of hidden variable theories such as local, crypto-nonlocal, contextual and non-local theories, along with several Bell like inequalities for these theories, providing theoretical proofs based on quantum mechanics for the falsification of some of these theories. Second we present a body of experimental, and theoretical works performed on a new class of Bell inequalities, i.e., the multiplicative Bell inequalities. We experimentally report the observation of the Bell parameters close to the Tsirelson (quantum) limit, upto a large number of measurement devices $(n)$, and compare the results with a particular deterministic strategy. We also obtain classical bounds for some $n$, and report the experimental violation of these classical limits. We theoretically derive new richer bounds on the CHSH inequality (named after John Clauser, Michael Horne, Abnor Shimony and Richard Holt) and the multiplicative Bell parameter for $n=2$, based on the principle of ``relativistic independence'', and experimentally observe the distribution of Bell parameters as predicted by these bounds.

It is known that quantum strategies change the range of possible payoffs for the players in the prisoner's dilemma. In this paper, we examine the effect of the degree of entanglement in determining the payoffs. When both players play quantum strategies, we show that the payoff for both players is unaffected by the entanglement value and it leads to a new Nash equilibrium.

All far-field optical imaging is limited by diffraction from optical elements, a phenomenon called Rayleigh's curse. It has been shown that through the use of the spatial mode demultiplexing technique (SPADE), an arbitrarily small separation between two point sources can be resolved, given a sufficiently large total number of photons N. This quantum metrology approach to super-resolution has since then been demonstrated and generalized to more complex situations. We propose a variant of SPADE, that we call biphoton SPADE, applied to imaging systems with spatially entangled photon pairs generated through spontaneous parametric downconversion. Our method can achieve a higher precision than SPADE, given any non-zero level of entanglement. We furthermore demonstrate our technique in a coincidence imaging setup and show super-resolution while only projecting on a select few of the total optimal modes in the 2D joint basis. Since the method uses quantum light and provides even further sensitivity to SPADE, it can potentially be used in the future for various light-sensitive imaging applications and in combination with neural networks. In nature, one often finds structures that have only been replicated by humans through years of precise, state-of-the-art engineering. Polymer spherulites, naturally occurring birefringent crystals that grow around defects in a radial pattern, are an example of this. We show through the example of ascorbic acid, commonly referred to as Vitamin C, that spherulites are capable of creating beams with orbital angular momentum (OAM) through a process called spin-to-orbit coupling. This action of the ascorbic acid crystals is analogous to the one of spatially structured waveplates called q-plates, which are built to have an azimuthally dependant optic axis. This opens the door for potentially cheaper fabrication of q-plates, and possibilities of tuning the growth of the molecules for arbitrary wavefront shaping with natural crystals. Finally, because of the wide range of crystals in the spherulite class, further investigation into different spherulites could shed light on the relationship between crystal symmetry and structure, and the shaping of light.

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No description available.

The North Atlantic right whale (Eubalaena glacialis) is the most endangered species of large whale in the world (IUCN). Efforts for the recovery of this species were initiated almost 20 years ago, yet the North Atlantic right whale shows little signs of recovery. Reliance on particular habitat areas and the effect of factors such as ship collisions, net entanglement and habitat disturbances are hampering the recovery of this species. Therefore, it is important to assess the level of genetic diversity left in this population and to identify and assess all habitat areas for potentially lethal threats. This study has identified a subset of the reproductive females that do not use the Bay of Fundy as a nursery area, through the genetic structuring of mtDNA control region haplotypes. Genetic structuring of the control region haplotypes was established and maintained by site fidelity of reproductive females to specific nursery areas. These results have identified a list of reproductive females that will be the targets of satellite tagging to elucidate the location of the alternative nursery area(s) to the Bay of Fundy. Analysis of mtDNA control region haplotypes in North and South Atlantic right whale has identified five haplotypes in the 180 North Atlantic right whales analyzed compared to 10 haplotypes in the 16 South Atlantic right whales analyzed. The low level ofhaplotypic variability in the North Atlantic right whale is a direct consequence of the extensive whaling period endured by this species. The genetic divergence between the North and South Atlantic right whales was estimated to have occurred 3.0-9.0 mya. This is similar to the genetic divergence of 2.0-5.3 mya found between the two clades identified in the South Atlantic samples. / Thesis / Master of Science (MSc)

This project investigates the possibility of expropriating the industrial infrastructure of a now defunct oil refinery for the bioremediation of toxic soils, restoration of functional riparian ecologies, and reinhabitation of the site by human and non-human life. The context of the project is based on the assumption that such an undertaking is highly unlikely under the current economic and political paradigm. As such it is situated in the distant future, the result of prolonged liberatory struggles over many generations. / Master of Architecture / On the shores of the Schuylkill River in Philadelphia, the largest and longest operating oil refinery on the east coast has been recently closed following a massive explosion. The 1300+ acre facility is heavily polluted and contaminated with a multitude of toxic chemicals. This project proposes using the existing refinery infrastructure in conjunction with biological processes to clean the contaminated soil and make the site fit for all types of life again. Riparian ecosystems (those at the edges of waterways) are some of the most important to planetary healthy, and as such are an important area of focus in repairing the damage wrought by large-scale industrial and petrochemical processes. Because these processes of repair and reinhabitation require long periods of time, this project is imagined in a distant future.

Quantum entanglement is widely renounced as one of the most fundamental concepts of quantum mechanics. Such phenomenon exhibit non-local interaction properties which cannot be explained classically. In this thesis, we address a number of problems associated with creating, transferring and engineering of entanglement between two separate parties. The work is motivated by a desire to better understand the dynamics of entanglement between systems. In particular, the research is mainly focused on the study of the dynamics of the well known maximally entangled Bell state under different influences such as decoherence and inter-qubit coupling. We show the connection between coherence and entanglement using the system sub jected to decoherence. We also confirm the transfer of entanglement between completely isolated partite using the double Jaynes-Cummings model. Based on this result, we propose a new conservation criterion proven to be general for single excitation systems. Such conservation criterion are then compared and extended to a general N qubit systems. In addition, an attempt is made to evaluate entanglement conservation rules for the EPR- like multipartite entanglement. We also describe a new technique for solving entanglement in the top-down way ignoring physical setup.

Quantum entanglement is widely renounced as one of the most fundamental concepts of quantum mechanics. Such phenomenon exhibit non-local interaction properties which cannot be explained classically. In this thesis, we address a number of problems associated with creating, transferring and engineering of entanglement between two separate parties. The work is motivated by a desire to better understand the dynamics of entanglement between systems. In particular, the research is mainly focused on the study of the dynamics of the well known maximally entangled Bell state under different influences such as decoherence and inter-qubit coupling. We show the connection between coherence and entanglement using the system sub jected to decoherence. We also confirm the transfer of entanglement between completely isolated partite using the double Jaynes-Cummings model. Based on this result, we propose a new conservation criterion proven to be general for single excitation systems. Such conservation criterion are then compared and extended to a general N qubit systems. In addition, an attempt is made to evaluate entanglement conservation rules for the EPR- like multipartite entanglement. We also describe a new technique for solving entanglement in the top-down way ignoring physical setup.