Graph Approach for Quantum Contextuality
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Transcript of Graph Approach for Quantum Contextuality
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Graph Approach for Quantum Contextuality
Marcelo Terra CunhaUniversidade Federal de Minas Gerais - UFMG
Brazil
IPQI - 2014Bhubaneswar, 28th February
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arXiv:1010.2163 arXiv: 1306.6289
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Adán CabelloSimone Severini
Andreas Winter
Barbara Amaral
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The Result
There is a translation from Non-Contextuality Inequalities into
Graph-Theoretical concepts
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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 Surprise
•The E-Principle can be such foundational stone
E = Exclusivity
Ernest Specker
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The Most Famous Case
Bell InequalitiesBell Scenario
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Bell InequalitiesLocal Correlations
Quantum Correlations
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The CHSH Scenario
J.F. Clauser, M.A. Horne, A. Shimony, and R.A. Holt,
Phys. Rev. Lett. 23, 880 (1969).
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The CHSH Graph
CompatibilityGraph
ExclusivityGraph
Beware: Lines are Cliques!
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CHSH Inequality
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CHSH Ineq. Graph
What is the relation?
Independencenumber
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KCBS Graphs
Exclusivity InequalityCompatibility
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Quantum Theory?
WhereOrthogonal Representation of
Handle
Lovász Theta Function
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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!
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Beautiful Geometry
Umbrela
Handle
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E-PrincipleThe sum of the probabilities of
pairwise exclusive events can notbe more than
FractionalPackingNumber
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The General Picture
where
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Questions?
Can you have a little more?
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Some Surprises
StockholmVienna
Global
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Collective BoundsSymmetry
Independency
E Principle
KCBS
We did not use Quantum Theory!
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More Results
•Sets in correlation space also have graph-theoretical analogues:
•NC = STAB
•Q = THETA
•E = QSTAB
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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)
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GeneralizationsGraph Approach to Nonlocality
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GeneralizationsGraph Approach to Nonlocality
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GeneralizationsGraph Approach to Nonlocality
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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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08/02/14
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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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