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Table of Contents
Intro
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 Lders' 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 the ``All-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
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 Lders' 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 the ``All-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