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Photonic Bell violation closing the fair-sampling loophole

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

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Photonic Bell violation closing the fair-sampling loophole

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  1. Photonic Bell violationclosing the fair-sampling loophole Max Planck Institute of Quantum Optics (MPQ) Garching / Munich, Germany Johannes Kofler Workshop “Quantum Information & Foundations of Quantum Mechanics” University of British Columbia, Vancouver, Canada 3 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 (outcome and setting independence) 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(,) • Simple 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 inequality • 300 seconds per setting combination • Detection efficiency tot75% • No background correction etc. • Photon: only system for which all main loopholes are now closed • (not yet simultaneously) 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)

  15. 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

  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)

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