1. Photonic Bell violation closing the fair-sampling loophole Workshop “Quantum Information & Foundations of Quantum Mechanics” University of British Columbia, Vancouver, Canada 3 July 2013 Johannes Kofler Max Planck Institute of Quantum Optics (MPQ) Garching / Munich, Germany

2. Overview Assumptions in Bell’s theorem  Realism  Locality  Freedom of choice Closing loopholes  Locality  Freedom of choice  Fair sampling Conclusion and outlook

3. Quantum mechanics and hidden variables 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) History

4. Local realism Realism:physical properties are (probabilistically) defined prior to and independent of measurement Locality:no physical influence can propagate faster than the speed of light External world Passive observers Classical world view:

5. Realism: Hidden variables determine global prob. distrib.: p(A a 1 b 1, A a 1 b 2, A a 2 b 1,…|λ) Locality: (OI)Outcome independence:p(A|a,b,B,λ) = p(A|a,b,λ)& vice versa for B (SI)Setting independence:p(A|a,b,λ) = p(A|a,λ) & vice versa for B Freedom of choice:p(a,b|λ) = p(a,b)  p(λ|a,b) = p(λ) λ Bell’s Assumptions Bell’s assumptions 1 J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978) 3 J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, p. 243 (2004) 1 2 3 2 J. S. Bell, Physics 1, 195 (1964)

6. Realism + Locality + Freedom of choice  Bell‘s inequality CHSH form 1 : S exp := E(a 1,b 2 ) + E(a 2,b 1 ) + E(a 2,b 1 ) – E(a 2,b 2 )  2 Original Bell paper 2 implicitly assumed 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 Assumptions Bell’s theorem 1 J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, PRL 23, 880 (1969) 2 J. S. Bell, Physics 1, 195 (1964)

7. Loopholes Why important? - quantum foundations - security of entanglement-based quantum cryptography Three main loopholes: Locality loophole hidden communication between the parties closed for photons (1982 1,1998 2 ) Freedom-of-choice loophole settings are correlated with hidden variables closed for photons (2010 3 ) Fair-sampling loophole measured subensemble is not representative closed for atoms (2001 4 ), superconducting qubits (2009 5 ) and for photons (2013 6 ) 1 A. Aspect et al., PRL 49, 1804 (1982) 2 G. Weihs et al., PRL 81, 5039 (1998) 3 T. Scheidl et al., PNAS 107, 10908 (2010) 4 M. A. Rowe et al., Nature 409, 791 (2001) 5 M. Ansmann et al., Nature 461, 504 (2009) 6 M. Giustina et al., Nature 497, 227 (2013) Loopholes: maintain local realism despite S exp > 2 E

8. Locality:A is space-like sep. from b and B B is space-like sep. from a and A T. Scheidl, R. Ursin, J. K., T. Herbst, L. Ratschbacher, X. Ma, S. Ramelow, T. Jennewein, A. Zeilinger, PNAS 107, 10908 (2010) Locality & freedom of choice b,Bb,B E,AE,A a Tenerife La Palma Freedom of choice:a and b are random a and b are space-like sep. from E E p(a,b| ) = p(a,b) p(A,B|a,b, ) = p(A|a, ) p(B|b, ) La PalmaTenerife

9. 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 Coincidence rate detected: 8 Hz Measurement time: 2400 s Number of total detected coinc.: 19200  Results T. Scheidl, R. Ursin, J. K., T. Herbst, L. Ratschbacher, X. Ma, S. Ramelow, T. Jennewein, A. Zeilinger, PNAS 107, 10908 (2010)

10. Fair-sampling loophole Unfair sampling:detection efficiency could be low and setting-dependent 1  A =  A ( , ),  B =  B ( , ) Simple local realistic model 2 : 1 P. M. Pearle, PRD 2, 1418 (1970) 2 N. Gisin and B. Gisin, Phys. Lett. A 260, 323 (1999) 3 I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, V. Scarani, V. Makarov, C. Kurtsiefer, PRL 107, 170404 (2011) Efficiency is not optional in security-related tasks (device-independent quantum cryptography): faked Bell violations 3 Reproduces the quantum predictions and has correct ratio of singles, coincidences and no clicks at all

11. Eberhard inequality CHSH inequality requires  tot > 82.8 % 1 (max. entangled states) Eberhard 2 (CH 3 ) inequality requires  tot > 66.7 %(non-max. ent. states)  no fair-sampling assumption  no requirement to measure  tot  no post-selection or normalization  only one detector per side 1 A. Garg and N. D. Mermin, PRD 35, 3831 (1987) 2 P. H. Eberhard, PRA 47, 747 (1993) 3 J. F. Clauser and M. A. Horne, PRD 10, 526 (1974) Source local realism

12. Transition-edge sensors 1 Picture from: Topics in Applied Physics 99, 63-150 (2005) 2 A. E. Lita, A. J. Miller, S. W. Nam, Opt. Express 16, 3032 (2008) Working principle: Superconductor (  200 nm thick tungsten film at  100 mK) at transition edge Steep dependence of resistivity on temperature Measurable temperature change by single absorbed photon Superconducting transition-edge sensors 1 Characteristics: High efficiency > 95 % 1 Low noise < 10 cps 1 Photon-number resolving

13. Setup Sagnac-type entangled pair source Non-max. entangled states Fiber-coupling efficiency >90% Filters: background- photon elimination >99% M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. K., J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, A. Zeilinger, Nature 497, 227 (2013)

14. Results M. Giustina, A. Mech, S. Ramelow, B. Wittmann, J. K., J. Beyer, A. Lita, B. Calkins, T. Gerrits, S. W. Nam, R. Ursin, A. Zeilinger, Nature 497, 227 (2013) Photon: only system for which all main loopholes are now closed (not yet simultaneously) C oo (α 1,β 1 )C oo (α 1,β 2 )C oo (α 2,β 1 )C oo (α 2,β 2 )SoA(α1)SoA(α1)SoB(β1)SoB(β1)J 1069306115259511911466974915228651693718–126715 Violation of Eberhard’s inequality 300 seconds per setting combination Detection efficiency  tot  75% No background correction etc.

15. The fair-sampling team Anton Zeilinger Marissa GiustinaAlexandra MechBernhard Wittmann Jörn BeyerAdriana LitaBrice CalkinsThomas Gerrits Sae Woo NamRupert Ursin Sven Ramelow

16. Conclusion and outlook Loopholes important for quantum foundations & quantum cryptography Locality and freedom-of-choice loophole closed for photons Fair-sampling loophole (already closed for atoms and superconducting qubits) now closed for photons Photons: first system for which each of the three major loopholes has been closed, albeit in separate experiments For a loophole-free experiment: fast random number generators, precise timing, efficiency gains to compensate propagation losses due to increased distance Endgame for local realism has begun

17. Appendix: Bell vs. Leggett-Garg J. K. and Č. Brukner, PRA 87, 052115 (2013)