1. Violation of local realism with freedom of choice Faculty of Physics, University of Vienna, Austria Institute for Quantum Optics and Quantum Information Austrian Academy of Sciences APS March Meeting Dallas, March 23rd 2011 Johannes Kofler, Thomas Scheidl, Rupert Ursin, Sven Ramelow, Xiao-song Ma, Thomas Herbst, Lothar Ratschbacher, Alessandro Fedrizzi, Nathan Langford, Thomas Jennewein, and Anton Zeilinger

2. Quantum mechanics and realism Bohr and Einstein, 1925 1927Kopenhagen interpretation (Bohr, Heisenberg) 1932von Neumann’s (wrong) proof of non-possibility of hidden variables 1935Einstein-Podolsky-Rosen paradox 1952De Broglie-Bohm (nonlocal) hidden variable theory 1964Bell‘s theorem on local hidden variables 1972First successful Bell test (Freedman & Clauser) Introduction

3. Realism: [J. F. Clauser & A. Shimony, Rep. Prog. Phys. 41, 1881 (1978)] Hidden variables λ determine outcome probabilities: p(A,B|a,b,λ) Realism: [J. F. Clauser & A. Shimony, Rep. Prog. Phys. 41, 1881 (1978)] Hidden variables λ determine outcome probabilities: p(A,B|a,b,λ) Locality: (OI)Outcome Independence:p(A|a,b,B,λ) = p(A|a,b,λ)& vice versa (SI)Setting Independence:p(A|a,b,λ) = p(A|a,λ) & vice versa Freedom of Choice:(FC) p(a,b|λ) = p(a,b)  p(λ|a,b) = p(λ) [J. S. Bell, Physics 1, 195 (1964)] [J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, p. 243 (2004)] λ Bell’s Assumptions

4. Realism + Locality + Freedom of Choice  Bell‘s Inequality CHSH form: |E(a 1,b 2 ) + E(a 2,b 1 ) + E(a 2,b 1 ) - E(a 2,b 2 )|  2 The original Bell paper (1964) implicitly assumes freedom of choice: A(a,b,B,λ)A(a,b,B,λ) locality (outcome and setting independence)  (λ|a,b) A(a,λ) B(b,λ) –  (λ|a,c) A(a,λ) B(c,λ) freedom of choice explicitly: implicitly: Bell’s Theorem

5. Locality loophole: There may be a communication from the setting or outcome on one side to the outcome on the other side Closed by Aspect et al., PRL 49, 1804 (1982) & Weihs et al., PRL 81, 5039 (1998) Fair-sampling loophole: The measured events stem from an unrepresentative subensemble Closed by Rowe et al., Nature 409, 791 (2001) Freedom-of-choice loophole: The setting choices may be correlated with the hidden variables Closed by Scheidl et al., PNAS 107, 10908 (2010) [this talk] Loopholes

6. (SI)  active setting choice + space-like separation of A (B) and b (a) (OI)  space-like separation of A and B x t E AB ab Special relativity:no physical signal can travel faster than light space-like separated events cannot influence each other Space-Time Requirements

7. (SI)  active setting choice + space-like separation of A (B) and b (a) (OI)  space-like separation of A and B x t E AB ab (FC)  random setting choices + space-like separation of a,b and E Special relativity:no physical signal can travel faster than light space-like separated events cannot influence each other Space-Time Requirements

8. 144 km Geography

9. 144 km B TenerifeLa Palma A x t E a b Locality: A is space-like separated from B (OI) and b (SI) B is space-like separated from A (OI) and a (SI) Freedom of choice: a and b are random and space-like separated from E Space-Time Diagram

10. 144 km Source 6 km fiber channel Alice 144 km free-space link Tenerife NOT QRNG 1.2 km RF link OGS La Palma 144 km free-space link Bob QRNG Geographic Details

11. Experimental Setup

12. Polarizer settings a, b0°, 22.5°0, 67.5°45°, 22.5°45°, 67.5° Correlation E(a,b)0.62 ± 0.010.63 ± 0.010.55 ± 0.01–0.57 ± 0.01 Obtained Bell value S exp 2.37 ± 0.02 F opt =0.91 ± 0.01 T=0.68 ± 0.04 Density matrix by state reconstruction: Coincidence rate detected: 8 Hz Measurement time: 2400 s Number of total coinc. detected: 19200  Experimental Results

13. Important Remarks In a fully deterministic world, neither the locality nor the freedom-of- choice loophole can be closed: Setting choices would be predetermined and could not be space-like separated from the outcome at the other side (locality) or the particle pair emission (freedom-of-choice). Thus, we need to assume stochastic local realism: There, setting choices can be created randomly at specific points in space-time. We have to consistently argue within local realism: The QRNG is the best candidate for producing stochastic settings.

14. We violated Bell’s inequality closing two loopholes in one experiment: First experiment to address and close (within reasonable assumptions) the freedom-of-choice loophole Simultaneously closed the locality loophole Now all three major loopholes – locality, fair-sampling, freedom-of-choice – have been closed individually A loophole-free Bell test is still missing Einstein and Bohr, 1930 Summary and Outlook

15. Rupert UrsinSven RamelowXiao-Song Ma Thomas Herbst Lothar RatschbacherAlessandro FedrizziNathan Langford Thomas JenneweinAnton Zeilinger Thomas Scheidl Acknowledgments