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Graph Approach for Quantum Contextuality. Marcelo Terra Cunha Universidade Federal de Minas Gerais - UFMG Brazil. IPQI - 2014 Bhubaneswar, 28th February. arXiv: 1306.6289. arXiv:1010.2163. Simone Severini. Adán Cabello. Andreas Winter. Barbara Amaral. The Result. - PowerPoint PPT Presentation
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Graph Approach for Quantum Contextuality
Marcelo Terra CunhaUniversidade Federal de Minas Gerais - UFMG
Brazil
IPQI - 2014Bhubaneswar, 28th February
arXiv:1010.2163 arXiv: 1306.6289
Adán CabelloSimone Severini
Andreas Winter
Barbara Amaral
The Result
There is a translation from Non-Contextuality Inequalities into
Graph-Theoretical concepts
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 Surprise
•The E-Principle can be such foundational stone
E = Exclusivity
Ernest Specker
The Most Famous Case
Bell InequalitiesBell Scenario
Bell InequalitiesLocal Correlations
Quantum Correlations
The CHSH Scenario
J.F. Clauser, M.A. Horne, A. Shimony, and R.A. Holt,
Phys. Rev. Lett. 23, 880 (1969).
The CHSH Graph
CompatibilityGraph
ExclusivityGraph
Beware: Lines are Cliques!
CHSH Inequality
CHSH Ineq. Graph
What is the relation?
Independencenumber
KCBS Graphs
Exclusivity InequalityCompatibility
Quantum Theory?
WhereOrthogonal Representation of
Handle
Lovász Theta Function
Small piece of History
•Zero-error information theory includes the concept of Shannon Capacity of a Graph
•Conjectured as intractable
•For the pentagon, a lower bound is very simple
•Lovász defined his function to be a computable upper bound
•And obtained the exact value for the pentagon!
Beautiful Geometry
Umbrela
Handle
E-PrincipleThe sum of the probabilities of
pairwise exclusive events can notbe more than
FractionalPackingNumber
The General Picture
where
Questions?
Can you have a little more?
Some Surprises
StockholmVienna
Global
Collective BoundsSymmetry
Independency
E Principle
KCBS
We did not use Quantum Theory!
More Results
•Sets in correlation space also have graph-theoretical analogues:
•NC = STAB
•Q = THETA
•E = QSTAB
More Results
•E-Principle gives the set of quantum correlations if this set is known for the complementary graph
•E-Principle forbids larger-than-quantum sets of correlationsBarbara Amaral, Marcelo Terra Cunha, and
Adán Cabello,Phys. Rev. A (2014)
GeneralizationsGraph Approach to Nonlocality
GeneralizationsGraph Approach to Nonlocality
GeneralizationsGraph Approach to Nonlocality
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
08/02/14
Take home messages
•Graph approach encodes all contextuality inequality and some generalizations
•Extensions to Nonlocality under construction
•E Principle is a good candidate for explaining quantum correlations
•No larger-than-quantum set!
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