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Space, Time and Q nonlocality

Nicolas GisinGroup of Applied Physics

Geneva universitySwitzerland

a + b= x.y

Alice Bobx

a b

y

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My early carrier as a physicist...

Geneva 1995

... my job consist in playingwith nonlocal correlations.

Aspect 1982

How does Nature manage to produce nonlocal correlations ???

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Locality

Assumptions: 1. Alice can freely choose her input x and can read her outcome a, and similarly for Bob;

2. x & y are independent of λλλλ: I(x: λλλλ) = I(y:λλλλ) = 0;3. locality: p(a,b|x,y,λλλλ) = p(a|x,λλλλ) · p(b|y,λλλλ).

Conclusion: Bell inequalities

λλλλ λλλλ

See e.g.arXiv:0901.4255

By far the most natural assumption !… refuted beyond (almost) any reasonable doubts.

Hence, quantum correlations happen, but the probabilities of their occurrence are not determined by local variables.

λλλλ=physical state of the system accordingto QM or to anyfuture theories.

NonlocalityNonlocalityNonlocalityNonlocality

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Satigny – Geneva – Jussy

18.0 km Jussy

Geneva

Satigny

δ

NNNN

SSSS

EEEEWWWW

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� When is a quantum measurement finished ?

� Possibly only once a macroscopic mass has significantly moved, as advocated e.g. by Diosi and Penrose.

� In usual Bell tests, detection events only trigger the motion of electrons of insufficient mass to finish the measurement process.

space

time

ar

inputbr

output αααα ββββ

Adrian Kent noticed that according to this plausible assumption, no Bell test so far ensured space-like separation !

J. Franson, PRD 31, 2529, 1985 A. Kent, arXiv:gr-qc/0507045

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He-Ne Laser

Piezo

+

-BS

Single-photondetector

4VPhotodiode

100 nmMirror

Mirror

- 1 0 1 2 3 4 5 6 7 8- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

1 . 5

2 . 0

2 . 5

3 . 0

3 . 5

4 . 0

4 . 5

- 3

0

3

6

9

1 2

1 5

1 8

2 1

2 4

2 7

3 0

Am

plitu

de (

V)

T i m e ( µ s )

Dis

tanc

e (n

m)

PR

L 100, 220404, 2008

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– Diósi’s equation

– For a parallelepiped mirror

– Numerical application in our case

Penrose-Diosi formula for collapse timeof the superposition: ψ1+ψ2

2223

dmG

Vd π

τ h=

sd µτ 1=310

6

10915.023

6.12

102

mmmmmmmV

nmd

kgm

−

−

⋅=××=

=⋅=

( )( )∫∫ −

−−=−

'

)'()'()()('

2

2

2

2

1

2

2

2

1332

1

rr

rrrrrdrd

Gmd

ψψψψτ

h

S. Adler, J.Phys. A40, 755 (2007)

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Bell test with true space-like separation

source

A B

time

space

The photon entersThe interferometer

A macroscopic mass hassignificantly moved

In usual Bell tests, detection events only trigger the motion of electrons of insufficient mass to finish the measurement process.

≈≈≈≈ 7 µµµµs

≈≈≈≈ 60 µµµµs≅≅≅≅ 18 km

quant-ph/0803.2425PRL100, 220404, 2008

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0 10 20 30 40 50 600

10

20

30

40

50

60

70

80

90

0

50000

100000

150000

200000

250000

300000

Coi

ncid

ence

s/60

s

Time (min)

Coincidences Sinusoidal fit: V=(90.5 ± 1.5)%

Sin

gles

(co

unts

/60s

)

Singles

Visibility > 90% ⇒⇒⇒⇒ nonlocal correlations between truly space-like separated events.

quant-ph/0803.2425PRL100, 220404, 2008

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How come the correlation ?

� How can these two locations out there in space-time know about each other ?

� via entanglement? (in Hilbert space) or

� via communication ? (in space-time)

� Let’s take the latter seriously. It requires to define faster than light “spooky action at a distance” in some preferred reference frame.

� If in this preferred frame the communication doesn’t arrive on time, then the correlation become local ! This can be tested.

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Let’s test these hypothetical preferred

reference frames

Alice and Bob, east-west orientation,perfect synchronization

with respect to earth⇒ perfect synchronization

w.r.t any frame movingperpendicular to theA-B axis

⇒ in 12 hours all hypothe-tical privileged framesare scanned.

A B

Ph. Eberhard, private communication

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0 30 60 90 120 150 180 210 2400

10

20

30

40

50

60

70

80

Coi

ncid

ence

s/60

s

Time (min)

Nature 454, 861, 2008

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0 3 0 6 0 9 0 1 2 0 1 5 0 1 8 05 0 0 0

7 5 0 0

1 0 0 0 0

2 5 0 0 0

5 0 0 0 0

7 5 0 0 0

1 0 0 0 0 0

2 5 0 0 0 0

Bo

und

on V

QI/c

χ (°)

Conclusion: the observed correlation is indeed truly nonlocal.

Indeed, to maintain a description based on spooky action at a distance, one would have to assume speeds even larger than thebound obtained in our experiment

PRL 88,120404,2002; J.Phys.A 34,7103,2001; Phys.Lett.A 276,1,2000

Bound assuming the Earth’s speed is ≤≤≤≤ 300 km/sNature 454, 861, 2008

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rsity1st Conclusion

From all the performed experiments one has to conclude that quantum correlations can’t be explained as time-ordered events.

⇒ There is no spooky action at a distance: there is not a first event that influences a second event.

⇒ Quantum correlation just happen, somehow from outside space-time :there is no story in space-time that tells us how it happens !

… or … the influences propagate at surprisingly large speeds

PRL 88,120404,2002; J.Phys.A 34,7103,2001; Phys.Lett.A 276,1,2000

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Let’s play more with nonlocal correlations

� Simulate quantum correlations with simple nonlocal correlations.

� Independent locality.

� Leggett inequality.

� Multi-partite nonlocality.

� nonlocal correlations as a resource(e.g. cryptographic keys), see V. Scarani and A. Acin this afternoon.

� etc

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a + b= x.y

Alice Bobx ∈{0,1}

a ∈{0,1} b ∈{0,1}

y∈{0,1}

a + b= x.y

Simulation with a PR-box

Prob(a=1|x,y) = ½, independent of y ⇒ no signaling

The PR-box is a strictly weaker resource than communication.

Found.Phys. 24, 379, 1994

See Nicolas Brunner this afternoon.

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Simulating a singlet with a PR-box

),|,(),|,(21212/ baPddbaPQM

rrrrrrrr ββββααααλλλλλλλλββββαααα λλλλλλλλππππθθθθ ∫∫∫∫========

)( ++= λβrr

bsgb

a + b= x.y

)()( 21 λλrrrr

asgasg + )()( −+ + λλrrrr

bsgbsg

)( 1λαrr

asga +=

2100

01)( λλλ

rrr±=

<≥

= ±andxif

xifxsg

PRL 94,220403,2005.For partial entanglemtsee PRA 78,052111,2008

where the are uniformly distributed on the sphereand is defined by the PR-box as follows:

jλλλλr

21λλλλλλλλP

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Independent Locality (bi-locality)

Alice Bob Charly

EPR 1 EPR 2

x y z

a b c

⇒⇒⇒⇒ P(a,b,c|x,y,z)

λλλλ1 λλλλ1 λλλλ2 λλλλ2

Independent locality (bi-locality) : I(λλλλ1:λλλλ2) = 0, or P(λλλλ1,λλλλ2)=P(λλλλ1)·P(λλλλ2)

⇒⇒⇒⇒ ??? Bell-like inequalities ???

Pbiloc.(a,b,c|x,y,z,λλλλ1,λλλλ2) = p(a|x, λλλλ1) · p(b|y, λλλλ1, λλλλ2) · p(c|z, λλλλ2)

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Independent Locality (bi-locality)

Alice Bob

EPR 1 EPR 2

x y

a b

λλλλ1 λλλλ1 λλλλ2

z

c

Charly

λλλλ2

The assumption of independent locality when the sources EPR1 and EPR2are independent is as natural as Bell’s locality assumption.

It is implicitly assumed in all Bell test with Quantum Random Number Generators (QRNG).

Random choice ofmeasurement setting

QRNG

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Entanglement Swapping between 2 totally autonomous cw sources

t±ττττ t t ±ττττ t ±ττττ

ττττ ττττ

Nature Physics3, 692, 2007

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2 totally autonomous cw sources

10 pm λλλλ-filters

∆λ∆λ∆λ∆λ = 70 nm

λλλλ = 1559 ±0.01 nm

Intensity:2-10% photon-pairper coherence time

Nature Physics3, 692, 2007

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Set of bi-local correlations

Polytope of local correlations

Pbiloc.(a,b,c|x,y,z) = ∫∫∫∫dλλλλ1ρρρρ(λλλλ1)∫∫∫∫dλλλλ ρρρρ(λλλλ2) p(a|x, λλλλ1) · p(b|y, λλλλ1, λλλλ2) · p(c|z, λλλλ2)

The vertices of thelocal polytope arealso bi-local

(λλλλ1,λλλλ2) (λλλλ’ 1,λλλλ’ 2)

Local, but NOT bi-local

The set of bi-local correlations is NOT convex,Its exact shape is unknown.

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Leggett’s “locality”

Leggett assumes that locally everything is “normal”, i.e. that individual particles are always in pure states:

),|,(),|,( baPdbaPQMrrrr βαλβα λθ ∫=

“Only” the correlations C µνµνµνµν are nonlocal. They just happen, without any classical explanation. They are only constraint by Pµνµνµνµν ≥≥≥≥ 0

Found.Phys. 10,1469,2003

( )),()()(14

1),|,( baCbMaMbaP BA

rrrrrr

λλλλ αββαβα ⋅+⋅+⋅+=⇒

non-signaling

( )),(14

1baCbaPrrrrrr

µννµµν αβσηβσηα

νµλ

⋅+⋅+⋅+=

⊗=

0 <η ≤ 1

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Leggett’s inequalities

(((( ))))BABA

BA

MMCMM

baCbMaMbaP

λλλλλλλλλλλλλλλλλλλλ

λλλλλλλλλλλλλλλλ αβαβαβαβββββααααββββαααα

−−−−−−−−≤≤≤≤≤≤≤≤++++++++−−−−⇔⇔⇔⇔

≥≥≥≥⋅⋅⋅⋅++++⋅⋅⋅⋅++++⋅⋅⋅⋅++++====

11

0),()()(141

),|,(rrrrrr

42

2cos2

2ϕϕϕϕϕϕϕϕ −−−−≈≈≈≈====QM

In strong contrast toBell’s inequalities, herethe bound depends on themeasurement settings

32

2sin

3

22)',(),(

3

1 ϕηϕη −≈−≤+⇒ ∑=xyzj

jjjj baCbaCrrrr

Modern formof Leggett’sinequality

⇒⇒⇒⇒ …

Branciard et al. Quant-ph/0801.2241Nature Physics 4, 681-685, 2008

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Experimental refutation of Leggett’s model

� integration time:4 x 15 sec / setting

� maximal violation:L=1.925 ± 0.0017(40.6 σ) at φ = -25°

L=1.922 ± 0.0017(38.1 σ) at φ = +25°

φ

L3

QM

Leggett

for 60 sec/setting:

L3(-30°)=5.7204±0.0028 (83.7 σ)

1.4

1.5

1.6

1.7

1.8

1.9

2

0-90° -60° -30° 30° 60° 90°

PRL 99,210406,2007PRL 99,210407,2007Branciard et al. Quant-ph/0801.2241Nature Physics 4, 681-685, 2008

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Multi-partite nonlocality bw n players

A1

x1

a1

A2

x2

a2

A3

x3

a3

An

xn

an

……

Objective: define and quantify the amount of multi-partite nonlocality

p(ai|xi)

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Multi-partite nonlocality bw n players

Example #1: grouping

How few groups m suffice in order for the n playersto reproduce the correlation p(ai|xi) with only shared randomness and communication inside each group (but no communicationin-between the different groups) ?

Example #2: broadcastingx1

a1How many players n-m have tobroadcast their inputs and outputsin order that the players can reproduce the correlation p(ai|xi) with only shared randomness ?

x2 x3 x4

a2 a3 a4

2/)(2 mnmnS −≤Theorem: arXiv:0903.2715

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Conclusions� Q nonlocality is a mature topic. Lots of progress have been achieved, but many important and fascinating questions are still open.

� Quantum correlations are very peculiar. They combine nonlocal correlations with non-trivial marginals in a way that is difficult to reproduce.

� Bell-type inequalities can be derived for all kinds of hypothesis, not only Bell locality, and all sorts of nonlocal resources.

� There are connections to experiments:- moving masses to ensure space-like separation- east-west Bell tests with good synchronization- asymmetric atom-photon entanglement

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Applications1...11)sin(0...00)cos( θθθ +=GHZ

0...100...010...

010...001...0

+++

+=W

k=2 parties that broadcastor m=n-2 groups suffice

n=65-pa

rtite

non

loca

l

4-pa

rtite

non

loca

l3-

part

ite n

onlo

cal

2-pa

rtite

non

loca

l

Fully n-partitenonlocal