hardy argument for quantum contextuality
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Hardy Argument for Quantum Contextuality
Marcelo Terra CunhaUniversidade Federal de Minas Gerais - UFMG
Brazil
IPQI - 2014Bhubaneswar, 25th February
The ProblemOr... Is there a Problem?
Consider measurements as revealingsome predefined quantities/properties
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
The Most Famous Case
Bell InequalitiesBell Scenario
Bell InequalitiesLocal Correlations
Quantum Correlations
Hardy Argument
Never
At Least
Yes
No
L. Hardy, PRL 68, 2981 (1992); 71, 1665 (1993).
Hardy Argument for “Nonlocality”
Special case of violation ofCHSH Bell inequality
Can we do it for the simplest contextuality
scenario?
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
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).
Hardy for KCBSNever
At Least
Yes
No
Hardy-like conditions
Hardy-KCBS with QT
Use Projectors
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
A Nice Surprise
Simon KocherErnest Specker
J. Math. Mech. 17, 59 (1967).
Generalizations
For all odd n ≥ 7
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
13/12/12
08/02/14
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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