Loophole-free test of Bell’s theorem with entangled photons Johannes Kofler Max Planck Institute of Quantum Optics (MPQ) Garching/Munich, Germany Indian Institute of Science Education and Research Mohali, India 14 Oct. 2016

Introduction Local realism: “objects have pre-existing definite properties & no action at a distance”  Bell’s inequality Relevant for foundations of quantum mechanics and (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)

History Quantum mechanics and hidden variables Kopenhagen interpretation (Bohr, Heisenberg, etc.) 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 First successful Bell test (Freedman & Clauser) since then Closing loopholes Bohr and Einstein (1925)

Local realism Classical world view: Realism: Physical properties are defined prior to and independent of measurement (via hidden variables) Locality: No physical influence can propagate faster than the speed of light External world Passive observers

Bell’s Assumptions Bell’s theorem Bell:1 Deterministic LHV: “Determinism”: “Locality”: Bell:2 Stochastic LHV: “Local causality”:  “Freedom of choice”:3 (“measurement independence”)  Local causality  Freedom of choice  Bell inequality 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)

Picture: Rev. Mod. Phys. 86, 419 (2014) Derivation of the CHSH inequality Dichotomic outcomes: Ai = A(ai,) = 1 Bj = B(bj,) = 1 A1 (B1 + B2) + A2 (B1 – B2) = 2 A1B1 + A1B2 + A2B1 – A2B2 = 2 S := A1B1 + A1B2 + A2B1 – A2B2  2 = locality SQM = 22 Picture: Rev. Mod. Phys. 86, 419 (2014) J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, PRL 23, 880 (1969)

Bell’s Assumptions Freedom of choice Local causality  Freedom of choice  X  specific Bell inequality Bell’s original derivation1 only implicitly assumed freedom of choice: explicitly: A(a,b,λ) B(a,b,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: original Bell paper:1 X = “Perfect anti-correlation”: A(b,λ) = –B(b,λ) CHSH:2 X = “Fair sampling” 1 J. S. Bell, Physics 1, 195 (1964) 2 J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, PRL 23, 880 (1969)

Loopholes Loopholes: maintain local realism despite exp. Bell violation Relevance – quantum foundations – quantum cryptography, randomness amplification/expansion

Locality Loophole addressed by space-time arrangement:1,2 26.05.2018 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 26.05.2018 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)

Locality & freedom of choice 26.05.2018 Locality & freedom of choice Tenerife b,B La Palma E,A a E Optical Ground Station, Tenerife Photo: ESA T. Scheidl et al. PNAS 107, 10908 (2010)

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 Local realistic models with unfair sampling2,3 SQM = 22 Reproduces the quantum predictions of the singlet state (with detection efficiency 2/3) Detection efficiency is not optional in security-related tasks: faked Bell violations4 1 P. M. Pearle, PRD 2, 1418 (1970) 2 F. Selleri & A. Zeilinger, Found. Phys. 18, 1141 (1988) 3 N. Gisin & B. Gisin, Phys. Lett. A 260, 323 (1999) 4 I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, V. Scarani, V. Makarov, C. Kurtsiefer, PRL 107, 170404 (2011)

Fair sampling Two options to close the loophole: Violate inequality that assumes fair sampling (e.g. CHSH) and show large total detection efficiency (> 82.8% for CHSH) Atoms1, superconducting qubits2 Violate inequality that does not assume fair sampling (e.g. CH, Eberhard, eff. 2/3) Photons3,4 1 M. A. Rowe et al., Nature 409, 791 (2001) 2 M. Ansmann et al., Nature 461, 504 (2009) 3 M. Giustina et al., Nature 497, 227 (2013) 4 B. G. Christensen et al., PRL 111, 130406 (2013)

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); (1),…,(k)) 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)

The Vienna experiment Source: polarization entangled photons, pulsed (1 MHz) type-II SPDC in Sagnac config. 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, PRA 93, 032115 (2016)

Results trials at 1 MHz, 3510 s measurement time, i.e. 3.5 billion trials one down-conversion pair in every 300 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) M. Giustina et al., PRL 115, 250401 (2015)

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)

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)