Bananaworld: Quantum Mechanics for Primates

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