Quantum walks with classically entangled light - Sephton, Bereneice B. (My University, 2018)
At the quantum level, entities and systems often behave counter-intuitively which we have come to describe with wave-particle duality. Accordingly, a particle that moves definitively from one position to another in our classical experience does something completely different on the quantum scale. The particle is not localized at any one position, but spreads out over all the possibilities as it moves. Here the particle can interfere with itself with wave-like propagation and generate, what is known as a Quantum Walk. This is the quantum mechanical analogue of the already well-known and used Random Walk where the particle takes random steps across the available positions, building up a series of random paths. The mechanics behind the random walk has already proved largely useful in many fields, from finance to simulation and computation. Analogously, the quantum walk promises even greater potential for development. Here, with many of the algorithms already developed, it would allow computations to outperform current classical methods on an unprecedented level. Additionally, by implementing these mechanics on various levels, it is possible to simulate and understand various quantum mechanical systems and phenomenon. This phenomenon consequently represents a significant advancement in several fields of study. Although there has been considerable theoretical development of this phenomenon, its potential now lies in implementing these quantum walks physically. Here, a physical system is required such that the quantum walk may be sustainably achieved, easily detected and dynamically altered as needed. Many systems have been subsequently proposed and demonstrated, but the criteria for a useful quantum walk leaves many such avenues lacking with the largest number of steps yet to reach 100 to the best of our knowledge. As a result, we explored a classical take on the quantum walk, utilizing the wave properties of light to achieve analogous mechanics with the advantage of the increased degree of control and robustness. While such an approach is not new, we considered a particular method where the quantum walk could be implemented in the spatial modes of light. By exploiting the non-separability (classical entanglement) of polarization and orbital angular momentum, such a classical quantum walk could be realized with greater intuitive implications and the potential for further study into the quantum mechanical nature of this phenomenon, over and above that of the other schemes, by walking the quantum-classical divide. The work presented here subsequently centres on experimentally achieving a quantum walk with classically entangled light for further development and useful implementation. Moreover, this work focused on demonstrating the sustainability, control and robustness necessary for this scheme to be beneficial for future development. In Chapter 1, an intuitive introduction is presented, highlighting the mechanics of this phenomenon that make it different from the Random walk counterpart. We also explore why this phenomenon is of such great importance with an overview of applications that physical implementation can result in. A more in-depth look into the dynamics and mathematical aspects of this walk is found in Chapter 2. Here a detailed look into the mechanisms behind the walk is taken with mathematical analysis. Furthermore, the subsequent differences and implications associated viii with utilizing classical light is explored, answering the question of what is quantum about the quantum walk. As the focus of this chapter is largely cemented in establishing a solid theoretical background, we also look into the physics behind classical light and develop the theoretical basis in the direction of structured light, with an emphasis on establishing classically entangled beams. Chapters 3 and 4 present the experimental work done throughout the course of this dissertation. With Chapter 3 we establish and characterize the elements necessary for obtaining a quantum walk in the spatial modes of light by utilizing waveplates as coins, q-plates as step operators and entanglement generators as well as mode sorters in a detection system. We also look into the characteristics of the modes that will be produced with these elements, allowing the propagation properties of the beam to be experimentally accounted for. In Chapter 4, we examine the experimental considerations of how to achieve a realistic and sustainable quantum walk. Here, we consider and implement the scheme proposed by Goyal et. al. [] where a light pulse follows a looped path, allowing the physical resources to be constant throughout the walk. We also show the experimental limitations of the equipment being utilized and the various steps needed to compensate. Finally, we not only implement a quantum walk with classically entangled light for the first time, but also demonstrate the flexibility of the system. Here, we achieve a maximum of 8 steps and show 5 different types of walks with varying dynamics and symmetry. The last chapter (Chapter 5) gives a summary of the dissertation in context of the goals and achievements of this work. The outlook and implications of these results are discussed and future steps outlined for extending this scheme into a highly competitive alternative for viable implementation of quantum walks for computing and simulation.
A dissertation submitted in fulﬁllment of the requirements for the degree of Masters in Science in the, The Structured Light Group Department of Physics, University of the Witwatersrand, Johannesburg, 2018
Keywords: Random walks (Mathematics); Quantum groups; Quantum computers