Max Planck Institute of Quantum Optics MPQ Garching

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

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

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

History Quantum mechanics and hidden variables 1927 Kopenhagen interpretation (Bohr, Heisenberg, etc. ) 1932 Von Neumann’s (wrong) proof of nonpossibility of hidden variables 1935 Einstein-Podolsky-Rosen paradox 1952 De Broglie-Bohm (nonlocal) hidden variable theory 1964 Bell’s theorem on local hidden variables 1972 First successful Bell test (Freedman & Clauser) Bohr and Einstein, 1925

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

Bell’s assumptions Assumptions Bell’s 1 Realism: Hidden variables determine global prob. distrib. : p(Aa 1 b 1, Aa 1 b 2, Aa 2 b 1, …|λ) 2 Locality: (OI)Outcome independence: (SI) Setting independence: factorizability: p(A|a, b, B, λ) = p(A|a, b, λ) = p(A|a, λ) & vice versa for B p(A, B|a, b, λ) = p(A|a, λ) p(B|b, λ) 3 Freedom of choice: (a, b|λ) = (a, b) (λ|a, b) = (λ) J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978) 2 J. S. Bell, Physics 1, 195 (1964) 1 3 J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, p. 243 (2004)

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

Loopholes: Why important? maintain local realism despite exp. Bell violation – quantum foundations – security of entanglement-based quantum cryptography 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 subensemble is not representative closed for atoms (20014), superconducting qubits (20095) and for photons (20136) 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) 1 E M. A. Rowe et al. , Nature 409, 791 (2001) M. Ansmann et al. , Nature 461, 504 (2009) 6 M. Giustina et al. , Nature 497, 227 (2013) 4 5

Locality & freedom of choice Tenerife b, B La Palma E, A a E La Palma Locality: Tenerife A is space-like sep. from b and B B is space-like sep. from a and A Freedom of choice: p(A, B|a, b, ) = p(A|a, ) p(B|b, ) a and b are random a and 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)

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) loophole 1 • Local realistic models 2, 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 violations 4 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) 1 4 I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, V. Scarani, V. Makarov, C. Kurtsiefer, PRL 107, 170404 (2011)

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 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 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) 1 3 4 J. F. Clauser and M. A. Horne, PRD 10, 526 (1974) P. H. Eberhard, PRA 47, 747 (1993)

Transition-edge sensors Working principle - Superconductor ( 200 nm thick tungsten film at 100 m. K) at transition edge - Steep dependence of resistivity on temperature - Measurable temperature change by single absorbed photon Characteristics - High efficiency > 95 %2 - Low noise < 10 Hz 2 - Photon-number resolving 1 2 Picture from: Topics in Applied Physics 99, 63 -150 (2005) A. E. Lita, A. J. Miller, S. W. Nam, Opt. Express 16, 3032 (2008) Superconducting transition-edge sensors 1

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)

Experimental results • Violation of Eberhard’s inequality 1 • 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) Exp. data 1 Model 2 Deviation C(a 1, b 1) C(a 1, b 2) C(a 2, b 1) C(a 2, b 2) SA(a 1) SB(b 1) J 1 069 306 1 068 886 – 0, 04 % 1 152 595 1 152 743 0, 01 % 1 191 146 1 192 489 0, 11 % 69 749 68 694 – 1, 51 % 1 522 865 1 538 766 1, 04 % 1 693 718 1 686 467 – 0, 43 % – 126 715 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, ar. Xiv: 1307. 6475 [quant-ph] (2013) 1

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 loophole 1 Local realistic model: Standard “moving windows” technique: coincidence if |TA(a, ) –TB(b, )| ½ a 2 b 2 coincidences are missed, CH/Eberhard violated 1 J. -Å. Larsson and R. Gill, EPL 67, 707 (2004)

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 a 2 b 2 coincidence-time loophole closed J. -Å. Larsson, M. Giustina, J. K. , B. Wittmann, R. Ursin, S. Ramelow, ar. Xiv: 1309. 0712 (2013)

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, ar. Xiv: 1309. 0712 (2013)

Conclusion and outlook Loophole: How to close: Locality space-like separate A & b, B and B & a, A a, b random Freedom of choice space-like separate E & a, b random Fair sampling (detection) use CHSH and also show > 82. 8% or use CH/Eberhard Coincidencetime use fixed time slots or window-sum method • Photons: each of the loopholes has been closed, albeit in separate experiments • Loophole-free experiment still missing but in reach

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