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Photonic Bell violation
closing the fair-sampling loophole
Workshop “Quantum Information & Foundations of Quantum Mechanics”
University of British Columbia, Vancouver, Canada
3 July 2013
Johannes Kofler
Max Planck Institute of Quantum Optics (MPQ)Garching / Munich, Germany
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Overview
• Assumptions in Bell’s theorem
- Realism
- Locality
- Freedom of choice
• Closing loopholes
- Locality
- Freedom of choice
- Fair sampling
• Conclusion and outlook
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Quantum mechanics and hidden variables
Bohr and Einstein, 1925
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)
History
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Local realism
• 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
Classical world view:
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Realism: Hidden variables determine global prob. distrib.: p(Aa1b1, Aa1b2, Aa2b1,…|λ)
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
Freedom of choice: p(a,b|λ) = p(a,b) p(λ|a,b) = p(λ)
λ
Bell’s AssumptionsBell’s assumptions
1 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
3
2 J. S. Bell, Physics 1, 195 (1964)
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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:
A(a,b,B,λ)
locality (outcome and setting independence)
(λ|a,b) A(a,λ) B(b,λ) – (λ|a,c) A(a,λ) B(c,λ)
freedom of choice
explicitly:
implicitly:
Bell’s AssumptionsBell’s theorem
1 J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, PRL 23, 880 (1969)2 J. S. Bell, Physics 1, 195 (1964)
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Loopholes
Why important?
- quantum foundations- security of entanglement-based quantum cryptography
Three main loopholes:
• Locality loopholehidden communication between the partiesclosed for photons (19821,19982)
• Freedom-of-choice loopholesettings are correlated with hidden variables closed for photons (20103)
• Fair-sampling loopholemeasured subensemble is not representativeclosed for atoms (20014), superconducting qubits (20095) and for photons (20136)
1 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)
4 M. A. Rowe et al., Nature 409, 791 (2001)5 M. Ansmann et al., Nature 461, 504 (2009)6 M. Giustina et al., Nature 497, 227 (2013)
Loopholes:
maintain local realism despite Sexp > 2
E
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Locality: A is space-like sep. from b and BB is space-like sep. from a and A
T. Scheidl, R. Ursin, J. K., T. Herbst, L. Ratschbacher, X. Ma, S. Ramelow, T. Jennewein, A. Zeilinger, PNAS 107, 10908 (2010)
Locality & freedom of choice
b,B
E,A
a
Tenerife
La Palma
Freedom of choice: a and b are random
a and b are space-like sep. from E
E
p(a,b|) = p(a,b)
p(A,B|a,b,) = p(A|a,) p(B|b,)
La Palma Tenerife
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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
Coincidence rate detected: 8 HzMeasurement time: 2400 s Number of total detected coinc.: 19200
Results
T. Scheidl, R. Ursin, J. K., T. Herbst, L. Ratschbacher, X. Ma, S. Ramelow, T. Jennewein, A. Zeilinger, PNAS 107, 10908 (2010)
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Fair-sampling loophole
Unfair sampling: detection efficiency could be low and setting-dependent1
A = A(,), B = B(,)
• Simple local realistic model2:
1 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)
• Efficiency is not optional in security-related tasks (device-independent quantum cryptography): faked Bell violations3
)sign(),(
aaA )sign(),(
bbB
||),(A
aabaBAbaE
S
BA2 2
d),(
1),(A
a
0),(A
a
1),(B
b
||),(B
bb
0),(B
b
:94
:94
:91
Reproduces the quantum predictions and has correct ratio of singles, coincidences and no clicks at all
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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
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)
0)()(),(),(),(),( 1122122111 Bo
Aooooooooo SSCCCCJ
Source
local realism
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Transition-edge sensors
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)
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
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Setup
• Sagnac-type entangled pair source
• Non-max. entangled states
• Fiber-coupling efficiency >90%
• Filters: background-photon elimination >99%
VHrHVr
r
21
1
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)
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Results
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)
0)()(),(),(),(),( 1122122111 Bo
Aooooooooo SSCCCCJ
Photon: only system for which all main loopholes are now closed(not yet simultaneously)
Coo(α1,β1) Coo(α1,β2) Coo(α2,β1) Coo(α2,β2) SoA(α1) SoB(β1) 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.
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The fair-sampling team
Anton Zeilinger
Marissa Giustina Alexandra Mech Bernhard Wittmann
Jörn Beyer Adriana Lita Brice Calkins Thomas Gerrits
Sae Woo Nam Rupert Ursin
Sven Ramelow
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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
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Appendix: Bell vs. Leggett-Garg
J. K. and Č. Brukner, PRA 87, 052115 (2013)