1. Hardy Argument for Quantum Contextuality
Marcelo Terra Cunha
Universidade Federal de Minas Gerais - UFMG
Brazil
IPQI
Bhubaneswar, 25th February

3. The Problem Or... Is there a Problem?
Consider measurements as revealing
some predefined quantities/properties

4. Envy about Relativity Theory
Personal Motivation
To clearly understand/explain the novelties that Quantum Theory brings
Try to “derive” Quantum Theory (or something like it) from other Principles
Envy about Relativity Theory

5. The Most Famous Case
Bell Inequalities
Bell Scenario

6. Bell Inequalities
Local Correlations
Quantum Correlations

7. Hardy Argument Never Yes At Least No
L. Hardy, PRL 68, (1992); 71, (1993).

8. Hardy Argument for “Nonlocality”
Special case of violation of
CHSH Bell inequality

9. Can we do it for the simplest contextuality scenario?

10. Simplest Contextuality Scenario
5 dychotomic questions
under cyclic compatibility conditions
Remark:
State-dependent contextuality
Note:
Beautiful History
Beautiful Geometry
A.A. Klyachko, M.A. Can, S. Binicioglu, and A.S. Shumovsky, PRL 101, (2008).

12. KCBS Scenario Five numbered boxes: 1, 2, 3, 4, 5
Each one, with or without a ball
Only neighbour boxes can be jointly open
A.A. Klyachko, M.A. Can, S. Binicioglu, and A.S. Shumovsky, PRL 101, (2008).

13. Hardy-like conditions
Hardy for KCBS
Never
At Least
Yes No
Hardy-like conditions

14. Hardy-KCBS with QT
Use Projectors

15. KCBS Inequality Hardy-like argument corresponds to a
non-maximal violation of KCBS
As well as Hardy’s original argument corresponds
to non-maximal violation of CHSH

16. A Nice Surprise Simon Kocher Ernest Specker
J. Math. Mech. 17, 59 (1967).

17. Generalizations
For all odd n ≥ 7

18. Pool: Next Friday Bit-Commitment arXiv:1307.0156
A protocol, using Bell Inequality violation, that avoids the no-go theorem of Lo- Chau-Mayers
Security is conjectural
Graph-Approach to Contextuality
Cabello, Severini & Winter idea for encoding NC Inequalities as graph-theoretical invariants;
Extensions,
E-Principle,
Quantum Correlations
Raise hands
Raise hands

19. 13/12/12

20. 08/02/14

21. Take home messages There is a Hardy argument for contextuality
Presumably, the simplest way to contextuality
It corresponds to a non-maximal violation of KCBS inequality
Its geometry is inside the bug

22. நன்றி
આભારદર્શક શબ્દો
ਧੰਨਵਾਦ ਹੈ
ধন্যবাদ
Grato
Thank you