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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Thank you

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