Bananaworld: Quantum Mechanics for Primates

Description

Nonlocality and quantum entanglement explained in terms of bananas. 1. Nobody Understands Quantum Mechanics 1.1 Quantum Blues 1.2 Why Bananaworld? 1.3 Yes! We Have No Bananas, But... 1.4 More 1.4.1 Special Relativity: The Basics 1.4.2 The Lorentz Transformation Notes 2. Qubits 2.1 About Light 2.2 Quantum States 2.3 Entangled Photons Notes 3. Bananaworld 3.1 Einstein-Podolsky-Rosen Bananas 3.2 Popescu-Rohrlich Bananas and Bell's Theorem 3.3 Simulating Popescu-Rohrlich Bananas 3.4 Loopholes 3.5 More 3.1.1 Some Useful Trigonometry 3.2.2 Correlations 3.3.3 Boolean Algebras Notes 4. Really Random 4.1 Correlation Arrays 4.2 Really Random Bananas 4.3 Really Random Qubits 4.4 More 4.4.l Simulating Entanglement in Bananaworld Notes 5. The Big Picture 5.1 No-Signaling Correlations 5.2 Classical Correlations Notes 6. Quantnun Magic 6.1 Greenberger-Horne-Zeilinger Bananas 6.2 The Aravind-Mermin Magic Pentagram 6.3 The Kochen-Specker Theorem and Klyachko Bananas 6.4 More 6.4.1 Simulating Greenberger-Horne-Zeilinger Bananas 6.4.2 Simulating Aravind-Mermin Bananas 6.4.3 Violating the Klyachko Inequality Notes 7. Quantum Secrets 7.1 Revealing Eve in Bananaworld 7.2 Revealing Eve in the Quantum World 7.3 Revealing Eve in a Device-Independent Scenario Notes 8. Quantum Feats 8.1 Quantum Computation 8.2 Quantum Teleportation 8.3 Superdense Coding 8.4 More 8.4.1 Two Quantum Algorithms Notes 9. Why the Quantum? 9.1 Information Causality 9.2 The Parable of the Over-Protective Seer 9..3 More 9.3.1 The Guessing Game 9.3.2 The Probability of Guessing Correctly 9.3.3 How Information Causality Works 9.3.4 The Tsirelson Bound from Information Causality Notes 10. Making Sense of It All 10.1 Schr\:odinger's Cat 10.2 The Measurement Problem 10.3 Pusey-Barrett-Rudolph Bananas 10.4 The Information-Theoretic Interpretation Notes Supplement: Some Mathematical Machinery Dirac's Ingenious Idea The Pauli Operators The Born Rule Noncommutativity and Uncertainty Entanglement Quantum Dynamics Relative Phase Informationally Complete Observables The Biorthogonal Decomposition Theorem States and Operators as Matrices Mixed States Index