A robust Bell inequality without two-outcome measurements

1. A robust Bell inequality without two-outcome measurements William Plick, PhD IQOQI Vienna APS March Meeting, March 6th, 2014

2. 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.

3. The Wigner Inequality Two Parties (+ + -, - - +) + (+ - -, - + +) Three settings (+ - -, - + +) + (+ - +, - + -) Perfect Anti-Correlations: (+ + -, - - +) (+ + -, - - +) + (- + -, - + -) (+ + -, - - +) + (+ - -, - + +) + (+ + -, - - +) + (- + -, - + -) +

4. 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 (+ + +, - - +) ?

5. Extending the Inequality How 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:

6. “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

7. Adding Counterfactuality + • + (+ - -, - - +) (+ - -, - + +) . . . (+ + +, + + +) • = Hidden Polarization “Click Pattern” Measurement Angles Bob’s Side

8. A Counterfactual Asymmetric Inequality Jerk Term Friendly Terms

9. Comparison to Other Inequalities

10. 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.

11. Acknowledgements Johannes Kofler Robert Fickler Sven Ramelow Anton Zeilinger RadekLapkiewicz ERC Advanced Grant: QIT4QAD

12. Thank you!