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Bell violation with entangled photons and without the fair-sampling assumption Foundations of Physics 2013 LMU Munich, Germany 30 July 2013 Johannes Kofler Max Planck Institute of Quantum Optics (MPQ) Garching / Munich, Germany

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Overview Assumptions in Bells theorem Realism Locality Freedom of choice Closing loopholes Locality Freedom of choice Fair sampling Conclusion and outlook

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Quantum mechanics and hidden variables Bohr and Einstein, Kopenhagen interpretation (Bohr, Heisenberg) 1932von Neumanns (wrong) proof of non-possibility of hidden variables 1935Einstein-Podolsky-Rosen paradox 1952De Broglie-Bohm (nonlocal) hidden variable theory 1964Bells theorem on local hidden variables 1972First successful Bell test (Freedman & Clauser) History

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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:

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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 Bells Assumptions Bells 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) J. S. Bell, Physics 1, 195 (1964)

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Realism + Locality + Freedom of choice Bells 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 (λ|a,b) A(a,λ) B(b,λ) – (λ|a,c) A(a,λ) B(c,λ) freedom of choice explicitly: implicitly: Bells Assumptions Bells 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)

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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, ) Freedom-of-choice loophole settings are correlated with hidden variables closed for photons ( ) Fair-sampling loophole measured subensemble is not representative closed for atoms ( ), superconducting qubits ( ) and for photons ( ) 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, (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

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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, (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

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Polarizer settings a, b0°, 22.5°0, 67.5°45°, 22.5°45°, 67.5° Correlation E(a,b)0.62 ± ± ± 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.: Results T. Scheidl, R. Ursin, J. K., T. Herbst, L. Ratschbacher, X. Ma, S. Ramelow, T. Jennewein, A. Zeilinger, PNAS 107, (2010)

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Fair-sampling loophole Unfair sampling:detection efficiency could be low and setting-dependent 1 A = A (, ), B = B (, ) 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, (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

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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

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Transition-edge sensors 1 Picture from: Topics in Applied Physics 99, (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

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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)

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Results 1 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) 2 J. K., S. Ramelow, M. Giustina, A. Zeilinger, arXiv: [quant-ph] (2013) Photon: only system for which all main loopholes are now closed (not yet simultaneously) Violation of Eberhards inequality seconds per setting combination Collection efficiency tot 75% No background correction etc. 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 Exp. data – Model Deviation–0,04 %0,01 %0,11 %–1,51 %1,04 %–0,43 %

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Production-rate loophole J. K., S. Ramelow, M. Giustina, A. Zeilinger, arXiv: [quant-ph] (2013) Strong drop of production rate (intensity) for 2 2 could lead to fake violation production rate loophole Comparison of all singles counts: Drifts slightly larger than purely statistical Normalization with respect to production rate: J – loophole closed in the experiment

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

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Conclusion and outlook Loopholes important for quantum foundations & quantum cryptography Locality (1982/98) and freedom-of-choice loophole (2010) closed for photons Fair-sampling loophole [already closed for atoms (2001) and superconducting qubits (2009)] 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

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

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