Graph Approach for Quantum Contextuality

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 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 Inequalities Bell 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 Beware: Lines are Cliques! Exclusivity Graph Compatibility Graph

CHSH Inequality

CHSH Ineq. Graph Independence number What is the relation?

Compatibility Inequality Exclusivity KCBS Graphs

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

The sum of the probabilities of pairwise exclusive events can not be more than E-Principle Fractional Packing Number

The General Picture where

Questions? Can you have a little more?

Some Surprises Global Vienna Stockholm

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

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 Correlations Raise 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!

நன்றி આભારદર્શક શબ્દો ਧੰਨਵਾਦ ਹੈ ধন্যবাদ धन्यवाद Thank you

Graph Approach for Quantum Contextuality