Photonic Bell violationclosing 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

Overview

• Assumptions in Bell’s theorem

- Realism

- Locality

- Freedom of choice

• Closing loopholes

- Locality

- Freedom of choice

- Fair sampling

• Conclusion and outlook

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

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:

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)

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)

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

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 randoma 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

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)

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

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

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

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)

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.

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

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)