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Quantum theory and the fundamental principle for quantum correlations (5)

Adán Cabello University of Sevilla. Quantum theory and the fundamental principle for quantum correlations (5). CIMPA research school on “Operator Theory and The Principles of Quantum Mechanics” , Faculté des Sciences, Université Moulay Ismail, Meknès, Maroc September 11 , 2014 (8:30).

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Quantum theory and the fundamental principle for quantum correlations (5)

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  1. Adán Cabello University of Sevilla Quantum theory and the fundamental principle for quantum correlations (5) CIMPA research school on “Operator Theory and The Principles of Quantum Mechanics”, Faculté des Sciences, Université Moulay Ismail, Meknès, Maroc September 11, 2014 (8:30)

  2. IV. The principle of quantum correlations

  3. Bell’s inequality

  4. Tsirelson’s bound

  5. Popescu-Rohrlich non-local non-signalling boxes

  6. Why?

  7. Forgot all you know about QT

  8. Let’s try to understand QT • Let’s try to understand the limits of quantum correlations without knowing QT

  9. The E principle • A theory satisfies the E principle when any set of pairwise mutually exclusive events is jointly (i.e., n-wise mutually) exclusive. • Therefore, from Kolmogorov’s axioms of probability, the sum of the probabilities of any set of pairwise mutually exclusive events cannot be higher than 1. • Important: The E principle cannot be derived from Kolmogorov’s axioms of probability.

  10. 3-box game • Maximize S=P(1,0|1,2)+P(1,0|2,3)+P(1,0|3,1)

  11. 3-box game • Maximize S=P(1,0|1,2)+P(1,0|2,3)+P(1,0|3,1) • Classical state: 3 boxes, one ball in one of them (the other 2 boxes empty). S=1.

  12. 3-box game • Maximize S=P(1,0|1,2)+P(1,0|2,3)+P(1,0|3,1) • Classical state: 3 boxes, one ball in one of them (the other 2 boxes empty). S=1. • Specker’s triangle state: Each of the probabilities is ½, S=3/2.

  13. Classical and Specker triangle states Classical state: S=1 Specker triangle state: S=3/2

  14. Specker’s observation

  15. Specker’s observation http://vimeo.com/52923835

  16. The E principle

  17. Specker’s observation implies the E principle

  18. Specker’s observation implies the E principle

  19. “The fundamental theorem of quantum mechanics”? http://vimeo.com/52923835

  20. Why?

  21. Consider two copies

  22. Consider two copies

  23. Consider two copies

  24. Consider two copies

  25. Vienna-Stockholm events 1010|1212 1010|5134 1010|2345 1010|4551 1010|3423

  26. Since the V and S experiments are independent

  27. E inequality #1 1010|1212 1010|5134 1010|2345 1010|4551 1010|3423

  28. E inequality #2

  29. E inequality #3

  30. E inequality #4

  31. E inequality #5

  32. Summing the 5 E inequalities

  33. E explains the whole Q set for the pentagon

  34. Applying the E principle to complementary graphs

  35. They are (vertex-transitive) complementary graphs

  36. Applying the E principle to complementary graphs

  37. We have an E inequality

  38. Applying the E principle to complementary graphs

  39. Rotate the second graph

  40. We have a second E inequality

  41. Rotate again the second graph

  42. Rotate again the second graph

  43. After 8 rotations, adding the 8 E inequalities

  44. How does the E principle work

  45. How does the E principle work

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