Quantum overlapping tomography based on linear optics

• Main Author: Yang, Zhengning
• Other Authors: Gao Weibo
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2023
• Subjects: Science::Physics
• Online Access: https://hdl.handle.net/10356/170876
• Institution: Nanyang Technological University

Quantum information science and technology is experiencing rapid development. The process raises an emerging demand for experiments to implement and demonstrate novel ideas to overcome the challenges towards the further application of quantum information. Linear optical systems have long been the most available and efficient platform for the demonstration of quantum information methods and concepts due to its robustness against the influence of environment. However, the large-scale multi-qubit linear optical information systems have long been suffering the low generated efficiency of the single photon sources, leading to a limited availability and scalability. In recent years, novel techniques such as beam-like SPDC open up new possibilities to break this bottleneck and further develop linear optical quantum information systems. Driven by the increasing demand and inspired by the technical progress, in my degree candidature, I carried out a project to build an advanced linear optical multi-qubit experimental platform to implement quantum information experiment and to discover novel methodologies of quantum optics research. In this thesis, I will present our progress and future perspectives. In Chapters 1-2, I will introduce the background and the motivation of this project first, and then present the basic concepts and principles of linear optical quantum information that are involved in my research. Chapter 3 describes my work on the generation and measurement of linear optical multi-qubit entanglement based on beam-like SPDC sources. By analyzing and containing the entanglement destruction from time-space correlation and group delay dispersion, the specifications of linear optical multi-qubit system can reach a higher level that allows for more applications. In Chapter 4, we discuss the methodology we developed to statistically estimate quantum states based on measurement results. In this project, we developed and applied a new algorithm named Bayesian mean estimation based on Gibbs sampling to estimate quantum states. I will describe the background, principle, and advantages compared to other widely accepted methods of this algorithm. In Chapter 5, I report our progress in experimentally demonstrating quantum overlapping tomography, a scheme focusing on characterizing critical information of a many-body quantum system in logarithmic time complexity. We compare the estimate results of full-state tomography and overlapping tomography to confirm that overlapping tomography gives accurate information of the system with much fewer state measurements than full-state tomography. Furthermore, under the condition that the system is too large to perform a tomography, we confirm that the state is still able to be measured with overlapping tomography. Chapter 6 begins with the conclusion of the thesis. Furthermore, I present outlooks on some potential directions to further increase the linear optical quantum information system.