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Supervisor's Foreword; Abstract; Acknowledgements; Contents; Preamble; What to Expect; 1 Introduction to Quantum Information; 1.1 Quantum States; 1.1.1 Qubits; 1.1.2 Beyond Qubits; 1.1.3 Comparing Quantum States; 1.1.4 Composite Systems and Entanglement; 1.2 Quantum Channels; 1.2.1 Working with Quantum Channels; 1.2.2 Process Matrix Representation; 1.3 Quantum Measurements; 1.3.1 Inconsistent Prescriptions; 1.3.2 Weak Measurements; 1.3.3 Quantum Non-demolition Measurements; 1.4 Quantum Information in Practice; 1.4.1 Single Photons; 1.4.2 Manipulating Polarization Qubits; References
2 Quantum Tomography2.1 Introduction; 2.2 Quantum State Tomography; 2.2.1 Linear Inversion Tomography; 2.2.2 Maximum Likelihood Estimation; 2.2.3 Zero Probabilities; 2.2.4 Error Bars for Quantum Tomography; 2.2.5 Quantum Process Tomography; 2.2.6 Caveats and Generalizations; 2.3 Taming Non-completely-Positive Maps with Superchannels; 2.3.1 Constructing the Superchannel mathcalM; 2.3.2 Superchannel Tomography; 2.3.3 Superchannels in the Wild; 2.3.4 Quantifying Initial Correlations; 2.3.5 Preparation Fidelity; 2.3.6 Discussion; References; 3 Introduction to Quantum Foundations
3.1 Probability and Randomness3.2 Quantum Correlations; 3.2.1 EPR Paradox; 3.2.2 Bell's Theorem; 3.2.3 A Hierarchy of Correlations; 3.2.4 Superquantum Correlations; 3.2.5 Correlation Polytopes; 3.3 Contextuality; 3.3.1 Kochen-Specker Contextuality; 3.3.2 Universal (Operational) Contextuality; 3.3.3 Noncontextuality and Classicality; 3.3.4 Wigner Negativity; 3.4 Paradoxes and Basic Games; 3.4.1 Quantum Teleportation; 3.4.2 GHZ Paradox and Multipartite Entanglement; 3.4.3 Hardy's Paradox; 3.4.4 Leggett-Garg and Macrorealism; 3.5 Pre- and Post-Selection Paradoxes; 3.5.1 Weak Values
2 Quantum Tomography2.1 Introduction; 2.2 Quantum State Tomography; 2.2.1 Linear Inversion Tomography; 2.2.2 Maximum Likelihood Estimation; 2.2.3 Zero Probabilities; 2.2.4 Error Bars for Quantum Tomography; 2.2.5 Quantum Process Tomography; 2.2.6 Caveats and Generalizations; 2.3 Taming Non-completely-Positive Maps with Superchannels; 2.3.1 Constructing the Superchannel mathcalM; 2.3.2 Superchannel Tomography; 2.3.3 Superchannels in the Wild; 2.3.4 Quantifying Initial Correlations; 2.3.5 Preparation Fidelity; 2.3.6 Discussion; References; 3 Introduction to Quantum Foundations
3.1 Probability and Randomness3.2 Quantum Correlations; 3.2.1 EPR Paradox; 3.2.2 Bell's Theorem; 3.2.3 A Hierarchy of Correlations; 3.2.4 Superquantum Correlations; 3.2.5 Correlation Polytopes; 3.3 Contextuality; 3.3.1 Kochen-Specker Contextuality; 3.3.2 Universal (Operational) Contextuality; 3.3.3 Noncontextuality and Classicality; 3.3.4 Wigner Negativity; 3.4 Paradoxes and Basic Games; 3.4.1 Quantum Teleportation; 3.4.2 GHZ Paradox and Multipartite Entanglement; 3.4.3 Hardy's Paradox; 3.4.4 Leggett-Garg and Macrorealism; 3.5 Pre- and Post-Selection Paradoxes; 3.5.1 Weak Values