Hardy Argument for Quantum Contextuality
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Transcript of Hardy Argument for Quantum Contextuality
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Hardy Argument for Quantum Contextuality
Marcelo Terra CunhaUniversidade Federal de Minas Gerais - UFMG
Brazil
IPQI - 2014Bhubaneswar, 25th February
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The ProblemOr... Is there a Problem?
Consider measurements as revealingsome predefined quantities/properties
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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
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The Most Famous Case
Bell InequalitiesBell Scenario
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Bell InequalitiesLocal Correlations
Quantum Correlations
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Hardy Argument
Never
At Least
Yes
No
L. Hardy, PRL 68, 2981 (1992); 71, 1665 (1993).
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Hardy Argument for “Nonlocality”
Special case of violation ofCHSH Bell inequality
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Can we do it for the simplest contextuality
scenario?
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Simplest Contextuality
Scenario
A.A. Klyachko, M.A. Can, S. Binicioglu, and A.S. Shumovsky, PRL 101, 020403 (2008).
5 dychotomic questionsunder cyclic compatibility conditions
Remark: State-
dependent contextuality
Note:Beautiful History
Beautiful Geometry
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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).
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Hardy for KCBSNever
At Least
Yes
No
Hardy-like conditions
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Hardy-KCBS with QT
Use Projectors
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KCBS Inequality
Hardy-like argument corresponds to a non-maximal violation of KCBS
As well as Hardy’s original argument correspondsto non-maximal violation of CHSH
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A Nice Surprise
Simon KocherErnest Specker
J. Math. Mech. 17, 59 (1967).
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Generalizations
For all odd n ≥ 7
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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
CorrelationsRaise hands Raise hands
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13/12/12
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08/02/14
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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
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