A robust Bell inequality without two-outcome measurements

William Plick, PhDIQOQI Vienna

APS March Meeting, March 6th, 2014

Why another inequality?Already so many!

This work started as an attempt to violate a local-realistic inequality in a very difficult experimental system.

The experiment in question had no access to dichotomic (two-outcome) measurements, and detections were extremely lossy.

No previously derived inequality was suitable.

The Wigner Inequality

Three settings

Two Parties

(+ + -, - - +)Perfect Anti-Correlations:

(+ + -, - - +) + (+ - -, - + +) (+ - -, - + +) + (+ - +, - + -) (+ + -, - - +) + (- + -, - + -)

(+ + -, - - +) + (+ - -, - + +) + (+ + -, - - +) + (- + -, - + -)

+ 34 ≤

14 +14

How Come I Haven’t Heard of It?Needs only single-outcome measurements.

Does not require use of the singles.

But, requires perfect anti-correlation in the proof itself.

What about symbols like (+ + +, - - +) ?

Extending the InequalityHow to make the inequality describe a real experiment?

(+ - -, - - +) + (+ - -, - + +) + . . . + (+ + +, + + +)

Some new terms cancel. Some can be bound from above:

(+ + +, + + +)

One new term in particular is a huge jerk:(+ - -, - - +)

“Half-Way” Result The “Jerk Term” prevents any useful inequality from being derived

without some assumptions.

However if we understand the physical system we can make very reasonable assumptions.

Original goal of derivation was to violate local-realism in a novel experimental system: entangled states of light with very high orbital angular momentum.

The way the system behaved was well understood so we could make some very reasonable assumptions and violate local realism in this system.

“An extension of the Wigner inequality: theory and experiment” arXiv:1304.2197 (2013) In review: PRA

Adding Counterfactuality

+ +(+ - -, - - +) (+ - -, - + +) . . . (+ + +, + + +)

=“Click Pattern” Measurement

AnglesBob’s Side Hidden

Polarization

A Counterfactual Asymmetric Inequality

Jerk Term Friendly Terms

Comparison to Other Inequalities

Review and Next Steps We have combined ideas from the Wigner inequality, counterfactual “Kochen-

Specker”-type arguments, and the (non-local) Leggett inequality into something wholly new.

Our inequality is asymmetric in its measurement requirements. One side must utilize photonic polarization modes. The other can be anything with some form of anti-correlation.

The inequality requires neither single-count rates, nor two-outcome measurements. No other inequality (to our knowledge) possesses both these characteristics.

What’s not yet known: efficiency requirements, the role of locality, and how far this formalism can be pushed.

Some other next steps: generalize to non-planar polarizations, extend the “Leggett Side” to another quantum-mechanical degree of freedom, etc.

Acknowledgements

Anton Zeilinger

Sven Ramelow Robert

Fickler

ADVANCEDGRANT: QIT4QADERC

Johannes Kofler

Radek

Lapkiewicz

Thank you!