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Closing loopholes in Bell tests of local realism Workshop Quantum Physics and the Nature of Reality International Academy Traunkirchen, Austria 22 November 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 Coincidence time Conclusion and outlook

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Acknowledgements Anton Zeilinger Marissa GiustinaBernhard Wittmann Sae Woo Nam Rupert Ursin Sven Ramelow Jan-Åke Larsson

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Quantum mechanics and hidden variables Bohr and Einstein, 1925 1927Kopenhagen interpretation (Bohr, Heisenberg, etc.) 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 factorizability: p(A,B|a,b,λ) = p(A|a,λ) p(B|b,λ) Freedom of choice: (a,b|λ) = (a,b) (λ|a,b) = (λ) Bells Assumptions Bells assumptions 1 J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978) 1 2 3 3 J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, p. 243 (2004) 2 J. S. Bell, Physics 1, 195 (1964)

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Realism + Locality + Freedom of choice + X Bells inequality Bells original derivation 1 only 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. S. Bell, Physics 1, 195 (1964) 2 J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, PRL 23, 880 (1969) B(a,b,A,λ)B(a,b,A,λ) Remarks:original Bell paper 1 :X = Perfect anti-correlation CHSH 2 :X = Fair sampling

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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 1,1998 2 ) Freedom-of-choice loophole settings are correlated with hidden variables closed for photons (2010 3 ) Fair-sampling (detection) 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 exp. Bell violation 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, 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

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Fair-sampling loophole Unfair sampling:Local detection efficiency is setting-dependent A = A (a, ), B = B (b, ) fair-sampling (detection) loophole 1 Local realistic models 2,3 1 P. M. Pearle, PRD 2, 1418 (1970) 2 F. Selleri and A. Zeilinger, Found. Phys. 18, 1141 (1988) 3 N. Gisin and B. Gisin, Phys. Lett. A 260, 323 (1999) Detection efficiency is not optional in security-related tasks (device-independent quantum cryptography): faked Bell violations 4 Reproduces the quantum predictions of the singlet state with detection efficiency 2/3 Fair sampling:Local detection efficiency depends only on hidden variable: A = A ( ), B = B ( ) observed outcomes faithfully reproduce the statistics of all emitted particles 4 I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, V. Scarani, V. Makarov, C. Kurtsiefer, PRL 107, 170404 (2011)

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CHSH vs. CH/Eberhard inequality CHSH inequality 1 two detectors per side correlation functions fair-sampling assumption used in derivation requires indep. verific. of tot > 82.8 % 2 maximally entangled states optimal 1 J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, PRL 23, 880 (1969) 2 A. Garg and N. D. Mermin, PRD 35, 3831 (1987) CH 3 (Eberhard 3 ) inequality only one detector per side probabilities (counts) no fair-sampling assumption in the derivation no requirement to measure tot impossible to violate unless tot > 66.7 % non-max. entangled states optimal 3 J. F. Clauser and M. A. Horne, PRD 10, 526 (1974) 4 P. H. Eberhard, PRA 47, 747 (1993)

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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 % 2 Low noise < 10 Hz 2 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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Experimental 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:1307.6475 [quant-ph] (2013) Photon: only system for which all main loopholes are now closed (not yet simultaneously) Violation of Eberhards inequality 1 300 seconds per setting combination Collection efficiency tot 75% No background correction etc. C(a1,b1)C(a1,b1)C(a1,b2)C(a1,b2)C(a2,b1)C(a2,b1)C(a2,b2)C(a2,b2)SA(a1)SA(a1)SB(b1)SB(b1)J Exp. data 1 1 069 3061 152 5951 191 14669 7491 522 8651 693 718–126 715 Model 2 1 068 8861 152 7431 192 48968 6941 538 7661 686 467 Deviation–0,04 %0,01 %0,11 %–1,51 %1,04 %–0,43 %

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The coincidence-time loophole 1 J.-Å. Larsson and R. Gill, EPL 67, 707 (2004) Unfair coincidences:Detection time is setting-dependent T A = T A (a, ), T B = T B (b, ) coincidence-time loophole 1 Fair coincidences:Local detection time depends only on hidden variable: T A = T A ( ), T B = T B ( ) identified pairs faithfully reproduce the statistics of all detected pairs Standard moving windows technique: coincidence if |T A (a, ) –T B (b, )| ½ a 2 b 2 coincidences are missed, CH/Eberhard violated Local realistic model:

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Closing the coincidence-time loophole J.-Å. Larsson, M. Giustina, J. K., B. Wittmann, R. Ursin, S. Ramelow, arXiv:1309.0712 (2013) a)Moving windows coincidence-time loophole open b)Predefined fixed local time slots coincidence-time loophole closed c)Triple window for a 2 b 2 coinc. coincidence-time loophole closed

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Application to experimental data J.-Å. Larsson, M. Giustina, J. K., B. Wittmann, R. Ursin, and S. Ramelow, arXiv:1309.0712 (2013) Moving windows coinc.-time loophole open Fixed time slots coinc.-time loophole closed Triple-window method coinc.-time loophole closed simultaneous closure of fair-sampling (detection) and coincidence-time loophole

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Conclusion and outlook Photons: each of the loopholes has been closed, albeit in separate experiments Loophole-free experiment still missing but in reach Loophole:How to close: Localityspace-like separate A & b,B and B & a,A a,b random Freedom ofspace-like separate E & a,b choicea,b random Fair samplinguse CHSH and also show > 82.8% (detection)or use CH/Eberhard Coincidence-use fixed time slots timeor window-sum method

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Loopholes hard/impossible to close Futher loopholes: Superdeterminism:Common cause for E and a,b Wait-at-the-source:E is further in the past; pairs wait before they start travelling Wait-at-the setting:a,b futher in the past; photons used for the setting choice wait before they start traveling Wait-at-the-detector:A,B are farther in the future, photons wait before detection, collapse locality loophole Actions into the past … E

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