Quantum theory and the fundamental principle for quantum correlations (6)

1. Adán Cabello University of Sevilla Quantum theory and the fundamental principle for quantum correlations (6) CIMPA research school on “Operator Theory and The Principles of Quantum Mechanics”, Faculté des Sciences, Université Moulay Ismail, Meknès, Maroc September 15, 2014 (14:30)

2. Bell inequalities

3. Inequalities for detecting true 3-body non-loc.

4. Non-contextuality inequalities

5. Quantum physicists obsessed by Tsirelson’s bound

6. Why?

7. Why?

8. Exclusivity graph for S

9. Let us assume that each of the 8 events has prob. p p p p p p p p p

10. Consider a Bell-CHSH experiment

11. Consider a second (independent) copy

12. Remember that the E graph of the CHSH inequality Vertices linked by an edge represent pairwise exclusive events

13. Is a subgraph of the graph of the CHSH scenario Events (nodes) in the same straight line or circumference are exclusive

14. If one assigns probability p to these 8 events p p p p p p p p

15. Normalization and co-measurability imply p p ½-p ½-p p p ½-p ½-p ½-p p ½-p p p ½-p p ½-p

16. Then, because independence

17. Now, in addition to the Bell-inequality measurements

18. One can measure A0A0’

19. One can measure A0A0’

20. Then, one can re-label the events as

21. If A0A0’ and A1A1’ are co-measurable

22. Then, one also has other type of events

23. Consider the following set of pairwise exclusive events

24. Similarly

25. Summing the 2 E inequalities

26. Assuming arbitrary probabilities for the 8 vertices • There are 16 tables.Summing them all, we get

27. Principles (2009)

28. Principles (2013)

29. What the principles explain

30. What the principles explain

31. What the principles explain

32. What the principles explain

33. What the principles explain

34. What the principles explain

35. Conclusion • The E principle explains more about quantum correlations than any other proposed principle.

36. Observation • The E principle explains more about quantum correlations than any other proposed principle. • The E principle is not an “information principle”, but a “logic principle” or a “probability principle”.

37. Open questions • The E principle explains more about quantum correlations than any other proposed principle. • The E principle is not an “information principle”, but a “logic principle” or a “probability principle”. • Is the E principle “the” principle of quantum correlations?

38. Open questions • The E principle explains more about quantum correlations than any other proposed principle. • The E principle is not an “information principle”, but a “logic principle” or a “probability principle”. • Is the E principle “the” principle of quantum correlations? • Why the E principle is not in any axiomatic formulation of QT?

39. Open questions • The E principle explains more about quantum correlations than any other proposed principle. • The E principle is not an “information principle”, but a “logic principle” or a “probability principle”. • Is the E principle “the” principle of quantum correlations? • Why the E principle is not in any axiomatic formulation of QT? • Is QT = Kolmogorov + E (with E nontrivial because “unperformed experiments have no results”)?

40. References • Graph-theoretic approach to quantum correlations • Multigraph refinement • The E principle