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(Aa1b1, Aa1b2, Aa2b1,…|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:
1
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)
2
J. S. Bell, Physics 1, 195 (1964)
Bell’s
Bell’s Assumptions
theorem
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:
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
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)
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)
M. Ansmann et al., Nature 461, 504 (2009)
6 M. Giustina et al., Nature 497, 227 (2013)
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°
Correlation E(a,b)
0.62 ± 0.01
0.63 ± 0.01
Obtained Bell value Sexp
45°, 22.5°
45°, 67.5°
0.55 ± 0.01 –0.57 ± 0.01
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-dependent1
A = A(,), B = B(,)
• Simple local realistic model2:
 
 
 
 
A(a,  )  sign(a   ) B(b ,  )  sign(b   )
 
 
 
4
:  A (a ,  )  | a   |
B (b ,  )  1
 
9
E (a , b ) 
 
 


4
:  A (a ,  )  1
B (b ,  )  | b   |
9
 
 
1
:  A (a ,  )  0
 B (b ,  )  0
9

S2

 
d
 A  B A B  a  b
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 violations3
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)
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
Source
J   Coo (1 , 1 )  Coo (1 ,  2 )  Coo ( 2 , 1 )  Coo ( 2 ,  2 )  S oA (1 )  S oB ( 1 )  0
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)
local realism
Transition-edge sensors
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
Characteristics:
• High efficiency > 95 %1
• Low noise < 10 cps1
• 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 sensors1
Setup
• Sagnac-type entangled
pair source
• Non-max. entangled
states
r 
1
1 r
2
 HV
 r VH

• 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
J   Coo (1 , 1 )  Coo (1 ,  2 )  Coo ( 2 , 1 )  Coo ( 2 ,  2 )  S oA (1 )  S oB ( 1 )  0
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.
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)