Closing loopholes in Bell tests of local realism

Workshop “Quantum Physics and the Nature of Reality”

International Academy Traunkirchen, Austria

22 November 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

- Coincidence time

• Conclusion and outlook

Acknowledgements

Anton Zeilinger

Marissa Giustina Bernhard Wittmann

Sae Woo Nam

Rupert Ursin

Sven Ramelow

Jan-Åke Larsson

Quantum mechanics and hidden variables

Bohr and Einstein, 1925

1927 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

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

factorizability: p(A,B|a,b,λ) = p(A|a,λ) p(B|b,λ)

Freedom of choice: (a,b|λ) = (a,b) (λ|a,b) = (λ)

Bell’s AssumptionsBell’s assumptions

1 J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978)

1

2

3

3 J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, p. 243 (2004)2 J. S. Bell, Physics 1, 195 (1964)

Realism + Locality + Freedom of choice + X Bell’s inequality

Bell’s original derivation1 only 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. S. Bell, Physics 1, 195 (1964)2 J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, PRL 23, 880 (1969)

B(a,b,A,λ)

Remarks: original Bell paper1: X = “Perfect anti-correlation”

CHSH2: X = “Fair sampling”

Loopholes

Why important?

– quantum foundations– security of entanglement-based quantum cryptography

Three main loopholes:

• Locality loopholehidden communication between the parties

closed for photons (19821,19982)

• Freedom-of-choice loopholesettings are correlated with hidden variables

closed for photons (20103)

• Fair-sampling (detection) loopholemeasured subensemble is not representative

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)5 M. Ansmann et al., Nature 461, 504 (2009)6 M. Giustina et al., Nature 497, 227 (2013)

Loopholes:

maintain local realism despite exp. Bell violation

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

Fair-sampling loophole

Unfair sampling: Local detection efficiency is setting-dependentA = A(a,), B = B(b,) fair-sampling (detection) loophole1

• Local realistic models2,3

1 P. M. Pearle, PRD 2, 1418 (1970)2 F. Selleri and A. Zeilinger, Found. Phys. 18, 1141 (1988)3 N. Gisin and B. Gisin, Phys. Lett. A 260, 323 (1999)

• Detection efficiency is not optional in security-related tasks (device-independent quantum cryptography): faked Bell violations4

)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 of the singlet state with detection efficiency 2/3

Fair sampling: Local detection efficiency depends only on hidden variable: A = A(), B = B() observed outcomes faithfully reproduce the statistics of all emitted particles

4 I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, V. Scarani, V. Makarov, C. Kurtsiefer, PRL 107, 170404 (2011)

CHSH vs. CH/Eberhard inequality

CHSH inequality1

- two detectors per side

- correlation functions

- fair-sampling assumption used in derivation

- requires indep. verific. of tot > 82.8 %2

- maximally entangled states optimal

1 J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, PRL 23, 880 (1969)2 A. Garg and N. D. Mermin, PRD 35, 3831 (1987)

0)()(),(

),(),(),(

1122

122111

bPaPbaP

baPbaPbaP

CH3 (Eberhard3) inequality

- only one detector per side

- probabilities (counts)

- no fair-sampling assumption in the derivation

- no requirement to measure tot

- impossible to violate unless tot > 66.7 %

- non-max. entangled states optimal

2),(),(),(),( 11122111 baEbaEbaEbaE

3 J. F. Clauser and M. A. Horne, PRD 10, 526 (1974)4 P. H. Eberhard, PRA 47, 747 (1993)

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 %2

- Low noise < 10 Hz2

- 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)

Experimental 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)()(),(),(),(),(:Eberhard 1122122111 bSaSbaCbaCbaCbaCJ BA

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.

C(a1,b1) C(a1,b2) C(a2,b1) C(a2,b2) SA(a1) SB(b1) J

Exp. 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 %

0)()(),(),(),(),(:CH 1122122111 bPaPbaPbaPbaPbaP

The coincidence-time loophole

1 J.-Å. Larsson and R. Gill, EPL 67, 707 (2004)

Unfair coincidences: Detection time is setting-dependentTA = TA(a,), TB = TB(b,) coincidence-time loophole1

Fair coincidences: Local detection time depends only on hidden variable: TA = TA(), TB = TB() identified pairs faithfully reproduce the statistics of all detected pairs

Standard “moving windows” technique: coincidence if |TA(a,) –TB(b,)| ½

0)()(),(

),(),(),(

1122

122111

bSaSbaC

baCbaCbaC

BA

a2b2 coincidences are missed, CH/Eberhard violated

Local realistic model:

Closing the coincidence-time loophole

J.-Å. Larsson, M. Giustina, J. K., B. Wittmann, R. Ursin, S. Ramelow, arXiv:1309.0712 (2013)

a) Moving windowscoincidence-time loophole open

b) Predefined fixed local time slotscoincidence-time loophole closed

c) Triple window for a2b2 coinc.coincidence-time loophole closed

Application to experimental data

J.-Å. Larsson, M. Giustina, J. K., B. Wittmann, R. Ursin, and S. Ramelow, arXiv:1309.0712 (2013)

Moving windowscoinc.-time loophole open

Fixed time slotscoinc.-time loophole closed

Triple-window methodcoinc.-time loophole closed

0)()(),(),(),(),(inequ. Eberhard 1122122111 bSaSbaCbaCbaCbaCJ BA

simultaneous closure of fair-sampling (detection) and coincidence-time loophole

Conclusion and outlook

• Photons: each of the loopholes has been closed, albeit in separate experiments

• Loophole-free experiment still missing but in reach

Loophole: How to close:

Locality space-like separate A & b,B and B & a,Aa,b random

Freedom of space-like separate E & a,bchoice a,b random

Fair sampling use CHSH and also show > 82.8%(detection) or use CH/Eberhard

Coincidence- use fixed time slotstime or window-sum method

0)()(),(

),(),(),(

1122

122111

bSaSbaC

baCbaCbaC

BA

Loopholes hard/impossible to close

Futher loopholes:

Superdeterminism: Common cause for E and a,b

Wait-at-the-source: E is further in the past; pairs wait before they start travelling

Wait-at-the setting: a,b futher in the past; photons used for the setting choice wait before they start traveling

Wait-at-the-detector: A,B are farther in the future, photons wait before detection, “collapse locality loophole”

Actions into the past…

E