#### Degree

Doctor of Philosophy (PhD)

#### Department

Physics and Astronomy

#### Document Type

Dissertation

#### Abstract

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 [1]. 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 [2]. 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 19^{th} and the early 20^{th} 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.

#### Recommended Citation

Valson Jacob, Kevin, "On Characterizing Quantum Processes and Detectors" (2020). *LSU Doctoral Dissertations*. 5221.

https://digitalcommons.lsu.edu/gradschool_dissertations/5221

#### Committee Chair

Dowling, Jonathan