Graph Approach for Quantum Contextuality Marcelo Terra Cunha Universidade Federal de Minas Gerais - UFMG Brazil IPQI Bhubaneswar, 28th February

arXiv: arXiv:

Adán Cabello Simone 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 Inequalities Local 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 Compatibility Graph Exclusivity Graph Beware: Lines are Cliques!

CHSH Inequality

CHSH Ineq. Graph What is the relation? Independence number

KCBS Graphs Exclusivity Inequality Compatibility

Quantum Theory? Where Orthogonal 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-Principle The sum of the probabilities of pairwise exclusive events can not be more than Fractional Packing Number

The General Picture where

Questions? Can you have a little more?

Some Surprises StockholmVienna Global

Collective Bounds Symmetry 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 correlations Barbara Amaral, Marcelo Terra Cunha, and Adán Cabello, Phys. Rev. A (2014)

Generalizations Graph Approach to Nonlocality

Generalizations Graph Approach to Nonlocality

Generalizations Graph Approach to Nonlocality

Pool: Next Friday Bit-Commitment arXiv: 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

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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