Max Planck Institute of Quantum Optics MPQ Garching

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

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

History Quantum mechanics and hidden variables 1927 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 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 λ 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: 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 3 Freedom of choice: p(a, b|λ) = p(a, b) p(λ|a, b) = p(λ) J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978) 3 J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, p. 243 (2004) 1 2 J. S. Bell, Physics 1, 195 (1964)

Bell’s Assumptions theorem Realism + Locality + Freedom of choice Bell‘s inequality CHSH form 1: Sexp : = E(a 1, b 2) + E(a 2, b 1) – E(a 2, b 2) 2 Original Bell paper 2 implicitly assumed freedom of choice: explicitly: A(a, b, B, λ) locality (outcome and setting independence) freedom of choice implicitly: (λ|a, b) A(a, λ) B(b, λ) – (λ|a, c) A(a, λ) B(c, λ) 1 2 J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, PRL 23, 880 (1969) J. S. Bell, Physics 1, 195 (1964)

Loopholes: Why important? maintain local realism despite Sexp > 2 - 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 loophole measured subensemble is not representative E 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 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 Tenerife Locality: A is space-like sep. from b and B B is space-like sep. from a and A p(A, B|a, b, ) = p(A|a, ) p(B|b, ) Freedom of choice: 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)

Results Coincidence rate detected: 8 Hz Measurement time: 2400 s Number of total detected coinc. : 19200 Polarizer settings a, b 0°, 22. 5° 0, 67. 5° 45°, 22. 5° 45°, 67. 5° Correlation E(a, b) 0. 62 ± 0. 01 0. 63 ± 0. 01 0. 55 ± 0. 01 – 0. 57 ± 0. 01 Obtained Bell value Sexp 2. 37 ± 0. 02 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 Unfair sampling: detection efficiency could be low and setting-dependent 1 A = A( , ), B = B( , ) • Simple local realistic model 2: 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 violations 3 P. M. Pearle, PRD 2, 1418 (1970) 2 N. Gisin and B. Gisin, Phys. Lett. A 260, 323 (1999) 3 I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, V. Scarani, V. Makarov, C. Kurtsiefer, PRL 107, 170404 (2011) 1

Eberhard inequality • CHSH inequality requires tot > 82. 8 %1 (max. entangled states) • Eberhard 2 (CH 3) inequality requires tot > 66. 7 % - no fair-sampling assumption - no requirement to measure tot - no post-selection or normalization - only one detector per side (non-max. ent. states) Source 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) 1 local realism

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 %1 • Low noise < 10 cps 1 • 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: backgroundphoton 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)

Results Coo(α 1, β 1) Coo(α 1, β 2) Coo(α 2, β 1) Coo(α 2, β 2) So. A(α 1) So. B(β 1) J 1069306 1152595 1191146 69749 1522865 1693718 – 126715 • 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)

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

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

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