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Bell violation with entangled photons and without the fair-sampling assumption

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

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Bell violation with entangled photons and without the fair-sampling assumption

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

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

  3. History Quantum mechanics and hidden variables • Kopenhagen interpretation • (Bohr, Heisenberg) • 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 • 1972 First successful Bell test (Freedman & Clauser) Bohr and Einstein, 1925

  4. 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

  5. Bell’s Assumptions Bell’s assumptions λ 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 3 Freedom ofchoice:p(a,b|λ) =p(a,b)  p(λ|a,b) =p(λ) 2 J. S. Bell, Physics1, 195 (1964) 1 J. F. Clauserand A. Shimony, Rep. Prog. Phys. 41, 1881 (1978) 3 J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, p. 243 (2004)

  6. Bell’s Assumptions Bell’s theorem Realism + Locality + Freedom of choice  Bell‘s inequality CHSH form1: Sexp := E(a1,b2) + E(a2,b1) + E(a2,b1) – E(a2,b2)  2 Original Bell paper2 implicitly assumed freedom of choice: explicitly: A(a,b,B,λ) locality freedom of choice (λ|a,b) A(a,λ) B(b,λ) – (λ|a,c) A(a,λ) B(c,λ) implicitly: 1J. 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 Loopholes: maintain local realism despite Sexp > 2 • 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 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)

  8. 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)

  9. Results Coincidence rate detected: 8 Hz Measurement time: 2400 s  Numberof total detectedcoinc.: 19200 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-dependent1 • A = A(,), B = B(,) • Local realistic model2: • Reproduces the quantum predictions and has correct ratio of singles, coincidences and no clicks at all • Efficiency is not optional in security-related tasks (device-independent quantum cryptography): faked Bell violations3 1 P. M. Pearle, PRD 2, 1418 (1970) 2 N. Gisin and B. Gisin, Phys. Lett. A 260, 323 (1999) 3I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, V. Scarani, V. Makarov, C. Kurtsiefer, PRL 107, 170404 (2011)

  11. Eberhard inequality • CHSH inequality requires tot > 82.8 %1 (max. entangled states) • Eberhard2 (CH3) 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 Source • local realism 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)

  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 %1 • Low noise < 10 cps1 • 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. 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. Production-rate loophole • 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  –123 000 •  loophole closed in the experiment J. K., S. Ramelow, M. Giustina, A. Zeilinger, arXiv:1307.6475 [quant-ph] (2013)

  16. The fair-sampling team Marissa Giustina Alexandra Mech Bernhard Wittmann Sven Ramelow Jörn Beyer Adriana Lita Brice Calkins Thomas Gerrits Sae Woo Nam Rupert Ursin Anton Zeilinger

  17. 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

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

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