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Closing loopholes in Bell tests of local realism

Closing loopholes in Bell tests of local realism. Max Planck Institute of Quantum Optics (MPQ) Garching / Munich, Germany. Johannes Kofler. Workshop “Quantum Physics and the Nature of Reality ” International Academy Traunkirchen , Austria 22 November 2013. Overview.

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Closing loopholes in Bell tests of local realism

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  1. Closing loopholes in Bell tests of local realism Max Planck Institute of Quantum Optics (MPQ) Garching / Munich, Germany Johannes Kofler Workshop “Quantum Physics and the Nature of Reality” International Academy Traunkirchen, Austria 22 November 2013

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

  3. Acknowledgements Sae Woo Nam Marissa Giustina Bernhard Wittmann Sven Ramelow Rupert Ursin Anton Zeilinger Jan-Åke Larsson

  4. History Quantum mechanics and hidden variables • Kopenhagen interpretation • (Bohr, Heisenberg, etc.) • 1932 Von Neumann’s (wrong) proof of non-possibility of hidden variables • 1935 Einstein-Podolsky-Rosen paradox • 1952 De Broglie-Bohm (nonlocal) hidden variable theory • Bell’s theorem on local hidden variables • First successful Bell test • (Freedman & Clauser) Bohr and Einstein, 1925

  5. Local realism Classical world view: • 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

  6. Bell’s Assumptions Bell’s assumptions 1 Realism: Hiddenvariables determine global prob. distrib.: p(Aa1b1, Aa1b2, Aa2b1,…|λ) 2 Locality: (OI) Outcomeindependence: p(A|a,b,B,λ) = p(A|a,b,λ) & viceversaforB (SI) Setting independence:p(A|a,b,λ) = p(A|a,λ) & viceversaforB  factorizability: p(A,B|a,b,λ) = p(A|a,λ)p(B|b,λ) 3 Freedom ofchoice:(a,b|λ) = (a,b)  (λ|a,b) = (λ) 3 J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, p. 243 (2004) 1 J. F. Clauserand A. Shimony, Rep. Prog. Phys. 41, 1881 (1978) 2J. S. Bell, Physics1, 195 (1964)

  7. Bell’s Assumptions Bell’s theorem Realism + Locality + Freedom of choice + X Bell’s inequality Bell’s original derivation1 only implicitly assumed freedom of choice: explicitly: A(a,b,B,λ) B(a,b,A,λ) locality freedom of choice (λ|a,b) A(a,λ) B(b,λ) – (λ|a,c) A(a,λ) B(c,λ) implicitly: Remarks: original Bell paper1: X = “Perfect anti-correlation” CHSH2: X = “Fair sampling” 1J. S. Bell, Physics 1, 195 (1964) 2J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt,PRL 23, 880 (1969)

  8. Loopholes • Why important? • – quantum foundations • – security of entanglement-based quantum cryptography Loopholes: maintain local realism despite exp. Bell violation • Three main loopholes: • Locality loophole • hidden communication between the parties • closed for photons (19821,19982) • Freedom-of-choice loophole • settings are correlated with hidden variables • closed for photons (20103) • Fair-sampling (detection) loophole • measured subensembleis not representative • closed for atoms (20014), superconducting qubits (20095) and for photons (20136) E 1 A. Aspect et al., PRL 49, 1804 (1982) 2 G. Weihset al., PRL 81, 5039 (1998) 3 T. Scheidlet al., PNAS 107, 10908 (2010) 4 M. A. Rowe et al., Nature 409, 791 (2001) 5 M. Ansmannet al., Nature 461, 504 (2009) 6M. Giustinaet al., Nature 497, 227 (2013)

  9. Locality & freedom of choice Tenerife b,B La Palma E,A E La Palma Tenerife a Locality: Ais space-like sep.from band B Bis space-like sep.from aand A p(A,B|a,b,) = p(A|a,)p(B|b,) Freedom of choice: aand bare random aand b are space-like sep. from E p(a,b|) = p(a,b) 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 • Fair sampling: Local detection efficiency depends only on hidden variable: A = A(), B = B()  observed outcomes faithfully reproduce the statistics of all emitted particles • Unfair sampling: Local detection efficiency is setting-dependent • A = A(a,), B = B(b,)  fair-sampling (detection) loophole1 • Local realistic models2,3 • Reproduces the quantum predictions of the singlet state with detection efficiency 2/3 • Detection efficiency is not optional in security-related tasks (device-independent quantum cryptography): faked Bell violations4 1 P. M. Pearle, PRD 2, 1418 (1970) 2F. Selleriand A. Zeilinger, Found. Phys. 18, 1141 (1988) 3 N. Gisin and B. Gisin, Phys. Lett. A 260, 323 (1999) 4I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, V. Scarani, V. Makarov, C. Kurtsiefer, PRL 107, 170404 (2011)

  11. CHSH vs. CH/Eberhard inequality • CHSH inequality1 • two detectors per side • correlation functions • fair-sampling assumption used in derivation • requires indep. verific. of tot > 82.8 %2 • maximally entangled states optimal • CH3 (Eberhard3) 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 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) 3J. F. Clauser and M. A. Horne, PRD 10, 526 (1974) 4P. H. Eberhard, PRA 47, 747 (1993)

  12. Transition-edge sensors • 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 sensors1 • Characteristics • High efficiency > 95 %2 • Low noise < 10 Hz2 • Photon-number resolving 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)

  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. Experimental results • Violation of Eberhard’s inequality1 • 300 seconds per setting combination • Collection efficiency tot 75% • No background correction etc. • Photon: only system for which all main loopholes are now closed • (not yet simultaneously) 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) 2J. K., S. Ramelow, M. Giustina, A. Zeilinger, arXiv:1307.6475 [quant-ph] (2013)

  15. The coincidence-time loophole • Fair coincidences: Local detection time depends only on hidden variable: TA= TA(), TB= TB() identified pairs faithfully reproduce the statistics of all detected pairs • Unfair coincidences: Detection time is setting-dependent • TA = TA(a,), TB = TB(b,)  coincidence-time loophole1 • Local realistic model: • Standard “moving windows” technique: coincidence if |TA(a,) –TB(b,)|  ½ • a2b2 coincidences are missed, CH/Eberhard violated 1 J.-Å. Larsson and R. Gill, EPL 67, 707 (2004)

  16. Closing the coincidence-time loophole • a) Moving windows • coincidence-time loophole open • b) Predefined fixed local time slots • coincidence-time loophole closed • c) Triple window for a2b2coinc. • coincidence-time loophole closed J.-Å. Larsson, M. Giustina, J. K., B. Wittmann, R. Ursin, S. Ramelow, arXiv:1309.0712 (2013)

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

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

  19. 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,bfuther 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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