Violation of local realismwith freedom of choice

Faculty of Physics,University of Vienna, Austria

Institute for Quantum Optics and Quantum InformationAustrian Academy of Sciences

APS March MeetingDallas, March 23rd 2011

Johannes Kofler, Thomas Scheidl, Rupert Ursin, Sven Ramelow,Xiao-song Ma, Thomas Herbst, Lothar Ratschbacher, Alessandro Fedrizzi,

Nathan Langford, Thomas Jennewein, and Anton Zeilinger

Quantum mechanics and realism

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 paradox1952 De Broglie-Bohm (nonlocal)

hidden variable theory1964 Bell‘s theorem on local hidden

variables1972 First successful Bell test

(Freedman & Clauser)

Introduction

[J. S. Bell, Physics 1, 195 (1964)]

[J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, p. 243 (2004)]

λ

Bell’s Assumptions

Realism + Locality + Freedom of Choice Bell‘s Inequality

CHSH form: |E(a1,b2) + E(a2,b1) + E(a2,b1) - E(a2,b2)| 2

The original Bell paper (1964) implicitly assumes 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 Theorem

Locality loophole:There may be a communication from the setting or outcome on one side to the outcome on the other sideClosed by Aspect et al., PRL 49, 1804 (1982) & Weihs et al., PRL 81, 5039 (1998)

Fair-sampling loophole:The measured events stem from an unrepresentative subensembleClosed by Rowe et al., Nature 409, 791 (2001)

Freedom-of-choice loophole:The setting choices may be correlated with the hidden variablesClosed by Scheidl et al., PNAS 107, 10908 (2010) [this talk]

Loopholes

(SI) active setting choice + space-like separation of A (B) and b (a)(OI) space-like separation of A and B

x

t

E

A B

a b

Special relativity: no physical signal can travel faster than light space-like separated events cannot influence each other

Space-Time Requirements

(SI) active setting choice + space-like separation of A (B) and b (a)(OI) space-like separation of A and B

x

t

E

A B

a b

(FC) random setting choices + space-like separation of a,b and E

Special relativity: no physical signal can travel faster than light space-like separated events cannot influence each other

Space-Time Requirements

144 km

Geography

144 kmB

TenerifeLa Palma

A

x

t

Ea

b

Locality:

A is space-like separated from B (OI) and b (SI)

B is space-like separated from A (OI) and a (SI)

Freedom of choice:

a and b are random and

space-like separated from E

Space-Time Diagram

144 km

Source6 km fiber channelAlice

144 km free-space link

Tenerife

NOT

QRNG

1.2 km RF linkOGS

La Palma

144 km free-space link

BobQRNG

Geographic Details

Experimental Setup

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

Fopt = 0.91 ± 0.01 T = 0.68 ± 0.04

Density matrix by state reconstruction:

Coincidence rate detected: 8 HzMeasurement time: 2400 s Number of total coinc. detected: 19200

Experimental Results

Important Remarks

• In a fully deterministic world, neither the locality nor the freedom-of-choice loophole can be closed:

Setting choices would be predetermined and could not be space-like separated from the outcome at the other side (locality) or the particle pair emission (freedom-of-choice).

• Thus, we need to assume stochastic local realism:

There, setting choices can be created randomly at specific points in space-time.

• We have to consistently argue within local realism:

The QRNG is the best candidate for producing stochastic settings.

• We violated Bell’s inequality closing two loopholes in one experiment:

First experiment to address and close (within reasonable assumptions) the freedom-of-choice loophole

Simultaneously closed the locality loophole

• Now all three major loopholes – locality, fair-sampling, freedom-of-choice – have been closed individually

• A loophole-free Bell test is still missing Einstein and Bohr, 1930

Summary and Outlook

Rupert Ursin Sven Ramelow Xiao-Song Ma Thomas Herbst

Lothar Ratschbacher Alessandro Fedrizzi Nathan Langford Thomas Jennewein Anton Zeilinger

Thomas Scheidl

Acknowledgments