A significant-loophole-free test of Bell’s theorem with entangled photons Johannes Kofler Max Planck Institute of Quantum Optics (MPQ) Garching/Munich, Germany PQE-2016 Snowbird, Utah, USA 4 Jan. 2016

The team Marissa Giustina Marijn A. M. Versteegh Sören Wengerowsky Johannes Handsteiner Armin Hochrainer Kevin Phelan Fabian Steinlechner Thomas Scheidl Rupert Ursin Bernhard Wittmann Anton Zeilinger Thomas Gerrits Adriana E. Lita L. Krister Shalm Sae Woo Nam Carlos Abellán Waldimar Amaya Valerio Pruneri Morgan W. Mitchell Jörn Beyer Jan-Åke Larsson Johannes Kofler Reference: Phys. Rev. Lett. 115, 250401 (2015)

Introduction Local realism: “objects have pre-existing definite properties & no action at a distance”  Bell’s inequality Relevant for (security of) modern quantum information protocols Quantum cryptography Randomness amplification / expansion Bell experiments have “loopholes” Locality Freedom of choice Fair sampling Coincidence time Memory Four “loophole-free” experiments in 2015 (Delft1, Boulder2, Vienna3, Munich) John S. Bell (1928–1990) 1 B. Hensen et al., Nature 526, 682 (2015) 2 L. K. Shalm et al., PRL 115, 250402 (2015) 3 M. Giustina et al., PRL 115, 250401 (2015)

Bell’s Assumptions Bell’s theorem Bell:1,2 “Local causality”: “Freedom of choice”:3 (“measurement independence”)  Local causality  Freedom of choice  Bell inequality Additional assumptions: original Bell paper:1 “Perfect anti-correlation”: A(b,λ) = –B(b,λ) CHSH:4 “Fair sampling” 1 J. S. Bell, Physics 1, 195 (1964) 3 J. F. Clauser & M. A. Horne, Phys. Rev. D 10, 526 (1974) 2 J. S. Bell, Epistemological Lett. 9 (1976) 4 J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, PRL 23, 880 (1969)

Locality Loophole addressed by space-time arrangement:1,2 23.11.2018 Locality Loophole addressed by space-time arrangement:1,2 Space-like separation between the outcomes (outcome independence) Space-like separation between each outcome and the distant setting (setting independence) Remark: Collapse locality loophole3 cannot be fully closed in principle 1 A. Aspect, P. Grangier, G. Roger, PRL 49, 91 (1982) 2 G. Weihs, T. Jennewein, C. Simon, H. Weinfurter, A. Zeilinger, PRL 81, 5039 (1998) 3 A. Kent, PRA, 012107 (2005)

Freedom of choice Loophole addressed by space-time arrangement:1,2 23.11.2018 Freedom of choice Loophole addressed by space-time arrangement:1,2 Space-like separation of setting choice events a,b and the pair emission event E (assuming that hidden variables are created at E) Remarks: Superdeterminism can never be ruled out Cosmic sources:3 1 T. Scheidl, R. Ursin, J.K., T. Herbst, L. Ratschbacher, X. Ma, S. Ramelow, T. Jennewein, A. Zeilinger, PNAS 107, 10908 (2010) 2 C. Erven, E. Meyer-Scott, K. Fisher, J. Lavoie, B. L. Higgins, Z. Yan, C. J. Pugh, J.-P. Bourgoin, R. Prevedel, L. K. Shalm, L. Richards, N. Gigov, R. Laflamme, G. Weihs, T. Jennewein, K. J. Resch, Nature Photon. 8, 292 (2014) 3 J. Gallicchio, A. S. Friedman, D. I. Kaiser, PRL 112, 110405 (2014)

Fair sampling 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 Two options to close the loophole: Violate inequality that assumes fair sampling (e.g. CHSH) and show large total detection efficiency (> 82.8% for CHSH2) Atoms3, superconducting qubits4 Violate inequality that does not assume fair sampling (e.g. CH, Eberhard, eff. 2/3) Photons5,6 1 P. M. Pearle, PRD 2, 1418 (1970) 3 M. A. Rowe et al., Nature 409, 791 (2001) 4 M. Ansmann et al., Nature 461, 504 (2009) 5 M. Giustina et al., Nature 497, 227 (2013) 6 B. G. Christensen et al., PRL 111, 130406 (2013) 2 A. Garg & N. D. Mermin, PRD 35, 3831 (1987)

Coincidence-time Unfair coincidences: Detection time is setting-dependent TA = TA(a,), TB = TB(b,)  coincidence-time loophole1 Moving windows coinc.-time loophole open Predefined fixed local time slots2 coinc.-time loophole closed3,4,5 1 J.-Å. Larsson and R. Gill, EPL 67, 707 (2004) 3 M. B. Agüero et al., PRA 86, 052121 (2012) 4 B. G. Christensen et al., PRL 111, 130406 (2013) 5 M. Giustina et al., Nature 497, 227 (2013) 2 J.-Å. Larsson, M. Giustina, J.K., B. Wittmann, R. Ursin, S. Ramelow, PRA 90, 032107 (2014)

Memory Memory: k-th outcome A(k) can depend on history: A(k) = A(k)(A(1),…,A(k–1); a(1),…,a(k); B(1),…,B(k–1); b(1),…,b(k–1)) similar for B(k)  memory loophole1,2,3 Two solutions: Space-like separated setups, used only once for each pair (unfeasible / impossible) ..... Drop assumption that trials are i.i.d. (independent and identically distributed) cannot use “standard” standard-deviation approach  “hypothesis testing”, e.g. supermartingales & Hoeffding‘s inequality 1 L. Accardi & M. Regoli, quant-ph/0007005; quantph/0007019; quant-ph/0110086 2 R. Gill, quant-ph/0110137, quant-ph/0301059 3 A. Kent, PRA 72, 012107 (2005)

Vienna experiment Source: pulsed (1 MHz) type-II SPDC in Sagnac configuration Detectors: superconducting transition edge sensors

Closing the locality & freedom-of-choice loopholes

Closing fair sampling, coincidence-time, memory CH-E inequality derived without the fair-sampling assumption: Can be violated with non-maximally entangled states Locally predefined fixed time-slots close the coincidence-time loophole Excess predictability of settings:   2  510–4 Requires adaptation of CH-E inequality:1 Closing memory loophole: Hoeffding’s inequality for J process 1 J. Kofler, M. Giustina, J.-Å. Larsson, M. W. Mitchell, arXiv:1411.4787

Results trials at 1 MHz, 3510 s measurement time, i.e.  3.5 billion trials one down-conversion pair in every 3500 trials total detection efficiency: 78.6% (Alice), 76.2% (Bob) state: r  –2.9, visibility > 99% (for product and singlet state) J-value: 7.2710–6 p-value: 3.7410–31 (probability that local realism could have produced the data by a random variation)

p-value versus excess predictability p-value of 3.7410–31 for characterized excess predictability   2.410–4 p-value remains below “gold standard” of 10–6 (dashed line) for  up to 0.65%

Conclusion Bell experiment using entangled photons Closing simultaneously the following loopholes: Locality Freedom of choice Fair sampling Coincidence time Memory Strong statistical violation Still requires assumptions (no super- determinism, classical rules of logic, etc)