Bell violation with entangled photonsand without the fair-sampling assumption

Foundations of Physics 2013LMU Munich, Germany

30 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

(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(,)

• 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

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)

2 J. K., S. Ramelow, M. Giustina, A. Zeilinger, arXiv:1307.6475 [quant-ph] (2013)

0)()(),(),(),(),( 1122122111 --- Bo

Aooooooooo SSCCCCJ

Photon: only system for which all main loopholes are now closed(not yet simultaneously)

• Violation of Eberhard’s inequality1

• 300 seconds per setting combination

• Collection efficiency tot 75%

• No background correction etc.

Coo(α1,β1) Coo(α1,β2) Coo(α2,β1) Coo(α2,β2) SoA(α1) SoB(β1) JExp. data1 1 069 306 1 152 595 1 191 146 69 749 1 522 865 1 693 718 –126 715Model2 1 068 886 1 152 743 1 192 489 68 694 1 538 766 1 686 467Deviation –0,04 % 0,01 % 0,11 % –1,51 % 1,04 % –0,43 %

Production-rate loophole

J. K., S. Ramelow, M. Giustina, A. Zeilinger, arXiv:1307.6475 [quant-ph] (2013)

0)()(),(),(),(),( 1122122111 --- Bo

Aooooooooo SSCCCCJ

• Strong drop of production rate (intensity) for 22 could lead to “fake violation”

“production rate loophole”

• Comparison of all singles counts:

• Drifts slightly larger than purely statistical

• Normalization with respect to production rate: J –123 000 loophole closed in the experiment

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 (1982/98) and freedom-of-choice loophole (2010) closed for photons

• Fair-sampling loophole [already closed for atoms (2001) and superconducting qubits (2009)] 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)