## Abstract

Quantum contextuality is one of the most intriguing and peculiar predictions of quantum mechanics. In layman’s terms, it refers to the fact that the result of a single measurement of a physical quantity in quantum mechanics depends on the

way the measurement is carried out. More precisely, the measurement outcome of an observable does not only reflect the pre-defined value of the observable itself; instead, the knowledge about the context—the set of compatible observables that are actually measured—is indispensable to determine the measurement result. Quantum contextuality is also a cornerstone in modern quantum information science. It is the origin of the famous quantum nonlocality and various nonclassical paradoxes. It is also a resource for many quantum information processing tasks and even universal quantum computing. Therefore, the study of quantum contextuality not only advances the comprehension of the foundations of quantum physics, but also facilitates the practical applications of quantum information technology.

In the last 15 years, the study of quantum contextuality has developed from a purely theoretical level to a stage where direct experimental tests become amenable. However, the experimental research on contextuality at the current stage largely focuses on direct validations of some most famous predictions of contextuality,while other forms of contextuality and its practical applications in quantum information science are rarely involved. The research in this thesis are committed to bridging this gap from two directions: (1) to construct and test stronger forms of contextuality and relieve the requirements of contextuality experiments on experimental platforms, and (2) to explore the connections between contextuality and the other concepts in quantum information science and directly demonstrate the application of contextuality in broader scenarios.

I will present the following aspects of research findings in this thesis.

The first topic is about the relationship between quantum contextuality and nonlocality. Since nonlocality is the manifestation of quantum contextuality in spacelikeseparated systems, it is possible to enhance the nonlocal quantum correlation caused by nonlocality by lifting the constraint of the spacelike-separation from the measurement operator. I have experimentally realised an example of quantum contextuality beyond nonlocality. At the same time, lifting the additional constraints could reduce the dimensionality of the state space required for demonstrating the quantum correlation. I have further constructed and experimentally realised the embedding of the strongest known quantum correlations into low-dimensional systems.

The second topic is regarding the “all-versus-nothing” paradoxes from quantum contextuality. Every logical proof of quantum contextuality can be transformed into an “all-versus-nothing” type quantum–classical paradox. The graph states are a class of highly entangled quantum states and the basic building blocks for measurementbased quantum computing. I have constructed and observed the “all-versus-nothing” paradox applicable to graph states, and show its applications in quantum state verification and the witness of quantum entanglement and quantum steering.

The third topic concerns the pre- and post-selection paradoxes from quantum contextuality. The investigation of quantum systems with pre- and post-selection provides additional information about its evolution process, which is reflected in the quantity called “weak values”. Quantum contextuality allows quantum processes to have strange behaviours; one example is the quantum Cheshire cat effect—the separation of the properties of a quantum system from the object itself. I have developed methods for weak value extraction without weak measurements to experimentally observe the exchange of grins between quantum Cheshire cats.

Finally, I will present the results of the topological protection and braiding dynamics of quantum contextuality in quasiparticle systems. The combination of quantum contextuality and the topological protection of quasiparticle systems is expected to pave the way for a universal fault-tolerant quantum computing architecture. I have studied the encoding of quantum information in parafermions—a type of quasiparticles—which topologically protects quantum information. I have designed and implemented a dedicated optical quantum simulator, in which the geometric phase from the braiding of parafermions, the topological protection of quantum contextuality resources, and the conservation properties of quantum contextuality in braiding operations are investigated to illustrate the potential of this system for universal fault-tolerant quantum computing.

The thesis is originally written in Chinese, and I have self-archived the Chinese version of the thesis on my website: https://manekimeow.github.io/document/zhliu_ PhDthesis.pdf. It is my great pleasure that I can present a translated version of the thesis to a broader audience one year after my graduation. I wish all the readers a nice experience in exploring the world of quantum contextuality.

way the measurement is carried out. More precisely, the measurement outcome of an observable does not only reflect the pre-defined value of the observable itself; instead, the knowledge about the context—the set of compatible observables that are actually measured—is indispensable to determine the measurement result. Quantum contextuality is also a cornerstone in modern quantum information science. It is the origin of the famous quantum nonlocality and various nonclassical paradoxes. It is also a resource for many quantum information processing tasks and even universal quantum computing. Therefore, the study of quantum contextuality not only advances the comprehension of the foundations of quantum physics, but also facilitates the practical applications of quantum information technology.

In the last 15 years, the study of quantum contextuality has developed from a purely theoretical level to a stage where direct experimental tests become amenable. However, the experimental research on contextuality at the current stage largely focuses on direct validations of some most famous predictions of contextuality,while other forms of contextuality and its practical applications in quantum information science are rarely involved. The research in this thesis are committed to bridging this gap from two directions: (1) to construct and test stronger forms of contextuality and relieve the requirements of contextuality experiments on experimental platforms, and (2) to explore the connections between contextuality and the other concepts in quantum information science and directly demonstrate the application of contextuality in broader scenarios.

I will present the following aspects of research findings in this thesis.

The first topic is about the relationship between quantum contextuality and nonlocality. Since nonlocality is the manifestation of quantum contextuality in spacelikeseparated systems, it is possible to enhance the nonlocal quantum correlation caused by nonlocality by lifting the constraint of the spacelike-separation from the measurement operator. I have experimentally realised an example of quantum contextuality beyond nonlocality. At the same time, lifting the additional constraints could reduce the dimensionality of the state space required for demonstrating the quantum correlation. I have further constructed and experimentally realised the embedding of the strongest known quantum correlations into low-dimensional systems.

The second topic is regarding the “all-versus-nothing” paradoxes from quantum contextuality. Every logical proof of quantum contextuality can be transformed into an “all-versus-nothing” type quantum–classical paradox. The graph states are a class of highly entangled quantum states and the basic building blocks for measurementbased quantum computing. I have constructed and observed the “all-versus-nothing” paradox applicable to graph states, and show its applications in quantum state verification and the witness of quantum entanglement and quantum steering.

The third topic concerns the pre- and post-selection paradoxes from quantum contextuality. The investigation of quantum systems with pre- and post-selection provides additional information about its evolution process, which is reflected in the quantity called “weak values”. Quantum contextuality allows quantum processes to have strange behaviours; one example is the quantum Cheshire cat effect—the separation of the properties of a quantum system from the object itself. I have developed methods for weak value extraction without weak measurements to experimentally observe the exchange of grins between quantum Cheshire cats.

Finally, I will present the results of the topological protection and braiding dynamics of quantum contextuality in quasiparticle systems. The combination of quantum contextuality and the topological protection of quasiparticle systems is expected to pave the way for a universal fault-tolerant quantum computing architecture. I have studied the encoding of quantum information in parafermions—a type of quasiparticles—which topologically protects quantum information. I have designed and implemented a dedicated optical quantum simulator, in which the geometric phase from the braiding of parafermions, the topological protection of quantum contextuality resources, and the conservation properties of quantum contextuality in braiding operations are investigated to illustrate the potential of this system for universal fault-tolerant quantum computing.

The thesis is originally written in Chinese, and I have self-archived the Chinese version of the thesis on my website: https://manekimeow.github.io/document/zhliu_ PhDthesis.pdf. It is my great pleasure that I can present a translated version of the thesis to a broader audience one year after my graduation. I wish all the readers a nice experience in exploring the world of quantum contextuality.

Original language | English |
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Publisher | Springer |
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Number of pages | 156 |

ISBN (Print) | 978-981-99-6169-6, 978-981-99-6166-5 |

ISBN (Electronic) | 978-981-99-6167-2 |

DOIs | |

Publication status | Published - 2023 |

Series | Springer Theses |
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ISSN | 2190-5053 |