Exploring Quantum Contextuality with Photons (Springer Theses)

✍ Scribed by Zheng-Hao Liu

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 170
• Category: Library

✦ Synopsis

This thesis highlights research explorations in quantum contextuality with photons.

Quantum contextuality is one of the most intriguing and peculiar predictions of quantum mechanics. It 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 fifteen 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 is committed to bridge 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. Specifically, the thesis have discussed the research topics about the relationship between quantum contextuality and nonlocality, the “all-versus-nothing” paradoxes from quantum contextuality, the ore- and post-selection paradoxes from quantum contextuality, and the topological protection and braiding dynamics of quantum contextuality in quasiparticle systems.

✦ Table of Contents

Supervisors’ Foreword
Preface
Acknowledgements
Contents
Acronyms
Part I Theoretical and Experimental Foundations
1 Prelude
References
2 Quantum Contextuality in a Nutshell
2.1 Mathematical Foundations of Quantum Mechanics
2.1.1 Quantum States, Evolution, and Observables
2.1.2 Quantum Measurements, Born's Rule, and Lüders' Rule
2.1.3 Gleason's Theorem
2.2 Hidden Variable Theories and Contextuality
2.2.1 The Kochen–Specker Theorem
2.2.2 Friend A's Confusion: The Peres–Mermin Square
2.2.3 Experimentally Testable Noncontextuality Inequality
2.2.4 Graph-Theoretic Approach to Contextuality
2.3 Contextuality in Quantum Information Science
2.3.1 Relation with the Reality of Wavefunction
2.3.2 Contradiction with Classical Causal Models
2.3.3 Role in Pre-post-selection Quantum Paradoxes
2.3.4 Interplay with Nonlocality
2.3.5 Application in Quantum Computation
References
3 Linear Optics Quantum Information
3.1 Encoding Quantum Information on Photons
3.1.1 Generation of Photon Pairs
3.1.2 Photonic Degrees of Freedom
3.2 Evolution and Operation of Photons
3.2.1 Operation of Polarization Qubits
3.2.2 Coupling of Polarization with other Degrees of Freedom
3.2.3 Imaginary-Time Evolution and Non-Hermitian Hamiltonians
3.3 Measurement of Optical Quantum States
3.3.1 Polarization Mode Measurement
3.3.2 Spatial Mode Measurement
3.3.3 Temporal Mode Discrimination
3.3.4 Orbital Angular Momentum Mode Detection
References
Part II Interplay Between Contextuality and Nonlocality
4 Stronger Contextuality Beyond Nonlocality
4.1 Nonlocality, Contextuality, and the Graph of Exclusivity
4.1.1 Case Study: Quantum Correlations in the Pentagon
4.2 Contextuality from Measurement-Repreparation Experiments
4.3 Contextuality Beyond Nonlocality
4.3.1 Sketch of the Theory
4.3.2 Experimental Implementation
4.4 Contextuality Concentration: Strongest Correlation in Lower Dimensions
4.4.1 Mermin Inequality: Exponential Quantum–Classical Gap
4.4.2 Reducing the Dimensionality of Measurements in the Mermin Inequality
4.4.3 Experimental Implementation
4.5 Summary
References
5 All-Versus-Nothing'' Contextuality in Graph States 5.1 Theoretical Foundations:All-Versus-Nothing'' Paradox and the Graph States
5.2 A Generic Construction of All-Versus-Nothing'' Contextuality in Graph State 5.2.1 Application: Quantum State Verification 5.3 Preparation of Four-Qubit Graph States 5.4 Observation and Applications of theAll-Versus-Nothing'' Paradox
5.4.1 Fidelity Estimation and Entanglement Witness
5.4.2 All-Versus-Nothing'' Paradox for Quantum Steering 5.5 Summary References Part III Contextuality in Quantum Information Science 6 Contextuality and Pre-post-selection Paradoxes: The Exchanged Grins Between Quantum Cheshire Cats 6.1 Tracking the Evolution Process of Quantum Systems 6.1.1 Two-State Vectors and Weak Values 6.1.2 An Example: Photon, Where have you Been? 6.2 Contextuality and the Quantum Cheshire Cat Paradox 6.2.1 Where is the Grin of the Quantum Cheshire Cat? 6.2.2 Finding the Quantum Cheshire Cat from the Peres–Mermin Square 6.2.3Quantum'' Cheshire Cat?
6.3 Quantum Cheshire Cats' Exchanged Grins
6.3.1 Observable and Pre- and Post-selection States
6.3.2 Weak Value Extraction Without Weak Measurement
6.3.3 Experimental Implementation
6.3.4 Experimental Results
6.4 Summary
References
7 Topologically-Protected Contextuality: Simulation of Photonic-Encoded Parafermions
7.1 From Parafermions to Optical Quantum Simulation
7.1.1 Mathematical Description of Parafermions
7.1.2 Braiding Operations of Parafermions
7.1.3 Quantum Simulation in Brief
7.1.4 Mapping Parafermions to Optical Systems
7.2 Optical Simulation of Parafermion Braiding Statistics
7.2.1 Designing a Dedicated Quantum Simulator
7.2.2 Experimental Results
7.3 From Contextuality to Universal Topological Quantum Computing
7.3.1 Dynamics of Contextuality Under Braiding Operations
7.3.2 Topologically-Protected Braiding of Parafermions
7.3.3 Noise-Resilience of Parafermion Contextuality
7.4 Conclusion
References
8 Postlude
References
Appendix A Case Study of Optical Quantum Information Experiment: Implementing Quantum Information Masking
A.1 Theoretical Foundation
A.2 Experimental Design
A.3 Results
A.4 Applications
References