A first meeting withBell’s Experiments

Valerio ScaraniCentre for Quantum Technologies &

Department of Physics, NUS

MY FIRST QUANTUM SHOCK

Why is quantum hard?

“ Because it’s too theoretical”

It describes the largest variety of phenomena at the highest degree of precision!

Indeed, all of this is quantum:

• Atomic and nuclear physics– From accelerators to power plants

• Chemistry– Why H2O is stable? Why periodic table?

• xx

Indeed, all this is quantum:

• Nuclei, atoms, molecules– All the particles discovered with accelerators…– The structure of the atoms, periodic table, radioactivity…– All of chemistry: why H2O is stable, why those reactions…

• “Solid state”– Why Copper conducts current, why Iron is magnetic…– Semiconductors in your chips, superconductors in high speed trains,

graphene…

• Light• The universe

– Big bang, cosmic background radiation– Energy of stars, and what happens when it finishes…

In fact, all of physics (only gravity is unclear)

Why is quantum hard? (2nd try)

“Because one has to master a lot of mathematics before understanding”

Maths Understanding??

Ask students if they feel they understand it, after

having learned about operators, eigenvalues

and the like…

Understanding without maths is possible!

NI XIAO AH!LIM PEI

UNDERSTAND QUANTUM PHYSICS!

“I can safely say that nobody understands quantum mechanics!”R.P. Feynman

In fact, Feynman DID, and many other people DO, understand it. But…

Maybe I can make a drawing?

… you cannot “make a drawing”!

User’s guide to the quantum world

• One cannot “make a drawing”, have a “mechanical” explanation hard to grasp

• But this means that Nature is more interesting than we expected

• It is worth while making the effort!

Time/effort devoted by the target public

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Classical analogs (light)

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MANY popular books Excellent textbooks

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EXPERIMENTS WITH PHOTONS

Polarization of photons

Classical light field

Light = Electric field propagating as a transverse wave

Polarization =direction of oscillation of the electric field

Quantum light field

• light is « made » of photons• polarization is a property of each photon• the state of polarization of the photon determines the direction of oscillation of the macroscopic field.

H-V basis

+45/-45 basis

How to measure polarization

I

Classical

Quantum: 1 photon

Polarizers = Filters

• Half intensity• New polarization state

I/2

I/2

I/4

I/4

I/2

0

p=1/2

p=1/2

« click »

TransmittedReflected

The polarization of a photon cannot be learned with

certainty

Two “entangled” photons

Laser

Non-linear crystal

“-1”“-1”

Bell experiment

Source of two entangled photons

“+1”“+1”

“-1”“+1”

Alice Bob

Observations (1): Alice

Alice

+1-1-1-1+1…

+1+1-1+1-1…

-1-1-1+1+1…

Prob(+1|A) = Prob(-1|A) = ½, for all A

Observations (2): Bob

-1-1+1-1+1…

+1-1-1-1+1…

-1+1+1+1-1…

Prob(+1|B) = Prob(-1|B) = ½, for all B

Bob

Observations (3): Alice & Bob

-1-1+1-1+1…

-1-1+1-1+1…

+1-1-1-1+1…

+1-1-1-1+1…

-1+1+1+1-1…

-1+1+1-1-1…

-1+1-1+1-1…

-1-1+1+1-1…

-1+1+1-1-1…

-1+1+1-1-1…

Similar bases “often” same results

Distant bases no correlationSame bases

same results

CORRELATIONS AT A DISTANCE HOW DO PHOTONS DO IT??

Explanation, first attempt: communication

Dear twin photon,I am going to be measured in the basis and shall give the result Pls behave accordingly.LOL

Will do, tks

Alice and Bob can be very distant: such a communication would have to propagate faster than the speed of light!

+1Basis output

-1

+1

+1Basis output

-1

+1

Explanation, second attempt:previous agreement

-1Basis output

+1

+1

-1Basis output

+1

+1Nice! It explains same basis same output

It cannot explain the correlations for “similar” bases. The proof is based on “Bell’s theorem”.

Bell’s theorem: proof

aBasis output

a’

bBasis output

b’

Assumption: a, a’, b and b’ exist one can compute: S = (a+a’)b + (a-a’)b’

Part 1: for all values of a, a’, b and b’, S=+2 or S=-2. Proof: if a=a’, …; and if a=-a’…

We cannot measure S in each shot, because we can choose only one basis; but we can measure <S> = <ab>+<a’b>+<ab’>-<a’b’>

Part 2: <S> 2. Proof: obvious

Quantum violation of <S>2

Correlations of entangled photons (please believe me here):

<ab> = cos(2( - )a b )a b

and for suitable choices of the measurements one can find

<S> = 22 2.8284 > 2

Bell’s theorem: if the outcomes are agreed in advance, <S>2

No mechanism!

The outcomes:• are correlated at a distance• NOT through communication• NOT through agreement

An experiment (Geneva, 1998)

Cornavin

Bellevue

Bernex

4.5

km

7.3 km

10.9

kmClassical

channels

R++R-+R+-R--

&KNbO 3

Flaser LP

Source

d1

8.1 km

9.3 km

quantum channel

quantum channeld2

APD1 -

APD 1 +

APD 2-

APD 2+

FS

ZFS

FM

FMZ

a

b

Results of the experiment

1000 4000 7000 10000 13000

-0.5

0.0

0.5

1.0

corr

ela

tion c

oeffi

cien

t

time [sec]

0

Vraw

= (85.3 ± 0.9)%

Vnet.

= (95.5 ± 1) %

Bell’s Thm: S 2

S(Q) = 2.8284

S(raw) = 2.41S(net) = 2.7

>2

cos 2( -a b)

CONSEQUENCES

Real randomness

“+1”“+1”

Alice Bob

-1

+1

+1

-1

+1

+1

Random!Random!

Secrecy

“+1”

Alice Bob

-1

+1

+1

-1

+1

+1

Private!Private!

“+1”

Eve

Summary

• Quantum correlations EXIST• There is no “mechanism” that

explains them– We can only predict probabilities– This is amazing…– … and is useful: randomness, secrecy