Doctor of Philosophy (PhD)
Physics and Astronomy
In 2009, physicists at the National Institute of Standards and Technology in Colorado, Boulder developed what could arguable be called the first rudimentary quantum computer . The past decade has seen unprecedented improvements in quantum information science culminating in the demonstration of quantum supremacy --- that quantum computers can solve problems that are impractical to be solved on the best supercomputers . This remarkable progress necessitates the development of techniques to characterize the quantum devices that are being developed. In my thesis, I will focus on such devices that manipulate and detect light.
In Chapter 1, I will introduce the reader to the historical underpinnings of the study of light. After surveying the history of light since time immemorial, I will delve into the developments in the study of light in the 19th and the early 20th century. I will then present a brief introduction to quantum mechanics. I end this chapter by demonstrating how light is quantized.
In Chapter 2, I will introduce the various tools necessary to delve into this dissertation. After defining quadrature operators and Wigner functions, I will introduce various states of light used in this thesis. I will then discuss how the evolution, as well as detection of quantum optical states, are modelled. I will then present the formalism of Gaussian quantum information that simplifies the manipulation of certain states of light. Finally, I will briefly talk about quantum metrology and show its advantage in phase estimation.
In Chapter 3, I will introduce a method to characterize linear and quadratically nonlinear optical systems. After motivating the need for this work, I will introduce the modifications necessary to the standard Mach-Zehnder interferometer in order to characterize optical systems with it. I will then show how to characterize linear optical systems with coherent probes. I will also show that this scheme is shot-noise limited. I will then show that by using single photons in addition, we can characterize quadratically nonlinear optical systems. Finally, I will show that no advantage is gained in sensitivity by using squeezed light along with coherent light as probes.
In Chapter 4, I will introduce a method to characterize photodetectors. This is done by developing an experimental method to find the Wigner functions of the POVM set corresponding to a photodetector. After motivating the necessity of this work as well as describing the proposed experimental setup, I will show how this scheme can be used to characterize a photon-number-resolving detector. I will then show that if we have some prior knowledge of the detector then it can drastically reduce the resource requirement of characterizing the detector. Finally, I will make the characterization robust against experimental noise by using tools from convex quadratic optimization.
At last, I summarize my conclusions in Chapter 5.
Valson Jacob, Kevin, "On Characterizing Quantum Processes and Detectors" (2020). LSU Doctoral Dissertations. 5221.