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Hardy Argument for Quantum Contextuality

Hardy Argument for Quantum Contextuality. Marcelo Terra Cunha Universidade Federal de Minas Gerais - UFMG Brazil. IPQI - 2014 Bhubaneswar, 25th February. The Problem. Or... Is there a Problem?. Consider measurements as revealing some predefined quantities/properties. Personal Motivation.

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Hardy Argument for Quantum Contextuality

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  1. Hardy Argument for Quantum Contextuality • Marcelo Terra Cunha • Universidade Federal de Minas Gerais - UFMG • Brazil IPQI - 2014 Bhubaneswar, 25th February

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

  3. 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

  4. The Most Famous Case Bell Inequalities Bell Scenario

  5. Bell Inequalities Local Correlations Quantum Correlations

  6. Yes No Hardy Argument Never At Least L. Hardy, PRL 68, 2981 (1992); 71, 1665 (1993).

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

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

  9. 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, 020403 (2008).

  10. 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, 020403 (2008).

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

  12. Hardy-KCBS with QT Use Projectors

  13. 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

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

  15. Generalizations For all odd n ≥ 7

  16. 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

  17. 13/12/12

  18. 08/02/14

  19. 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

  20. நன்றி આભારદર્શક શબ્દો ਧੰਨਵਾਦ ਹੈ ধন্যবাদ Grato Thank you

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