Experimental Quantum Teleportation

7/28/2019 Experimental Quantum Teleportation

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Experimental Quantum Teleportation

Quantum systems forInformation Technology

Kambiz Behfar

Phani Kumar


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Contents

Concept of Quantum Teleportation

Introduction

Quantum Teleportation CircuitTheoretical Results

Experimental RealizationPrinciples

Entangled StatesOutside Teleportation Region

Inside Teleportation Region

Measured Coincidence Rate

Summary


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Quantum Teleportation

Teleportation:

Teleportation means: a person or object disappear while an exact replica appears in the best case immediately at somedistant location.

Bennett et al. (1993) have suggested that it is possible to transfer the quantum state of a particle onto another particle-theprocess of quantum teleportation-provided one does not get any information about the state in the course of thistransformation.

Application:

Teleportation can be used in place of wiring in a large quantum computer.

To Build a distributed system (e.g. a quantum multicomputer).

and so on


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Quantum Teleportation Circuit

( 01 10 ) / 2Y = -

( ) ( )

( ) ( )

( 01 10 ) 0 1 ( 01 10 ) 0 11

2 ( 00 11 ) 1 0 ( 00 11 ) 1 0

( 01 10 )

( 01 10 )1

( 00 11 )2

( 00 11 )

a b a by a b a byyyy

-

- - + + - + +

Y =

- + + + -

- - +

+ - +

+ +

+

Z

X

XZ

H

X

M2

Z

M1

-

Y

M1

M2

0 1a b= +


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Proof

( )

( )( )

( )

( 00 11 ) / 2 ( 00 11 ) 1 0 001 000 111 110

( 00 11 ) / 2 ( 00 11 ) 1 0 001 000 111 110

( 01 10 ) / 2 ( 01 10 ) 0 1 010 011 100 101

( 01 10 ) / 2 ( 01 10 ) 0 1 010 011 100 1

Expanding RHS

y a b a b a by a b a b a by a b a b a by a b a b a b

+ = + - = - + -

- = - + = + - -

+ - = + - + = - + + +

- - = - - - = - - - +

XZ

X

Z

01

001 110 010 101b a b

- - - - - - - - - - - - - - - - - - -

- - +

( 01 10 ) / 2 ( 01 10 ) / 2

( 00 11 ) / 2 ( 00 11 ) / 2

1( 0 1 ) ( 01 10 ) 001 110 010 1012

Expanding LHS

y y y y y

y a b a b a b

- - + - +

+ -

+ -

-

Y = Y - + Y - + F + F

Y = + Y = -

F = + F = -

Y = + + = - - +

Z X XZ


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QT Circuit


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A complete Bell-state measurement can not only give the result that the two particles 1and 2 are in the anti-symmetric state, but with equal probabilities of 25% we could findthem in any one of the three other entangled states.

After successful teleportation particle 1 is not available in its original state any more,and therefore particle 3 is not a clone but is really the result of teleportation.

-F

+

Y

00

01

10

11

obtaining

ZX

Z

X

I

So Bobapplies gate

Then Bobs

qubit is in

state

If Aliceobtains

10

01

10

01

10

-

Y

+

F

Theoretical Results


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Principle of Quantum Teleportation Alice has particle 1

Alice & Bob share EPR pair

Alice performs BSM causingentanglement between photon1 and 2

Alice sends classicalinformation to Bob

Bob performs unitarytransformation

Teleporting the state not theparticle

Correlations used for datatransfer

Schematic idea for quantum teleportation introducing Alice as a sending and Bob as

a receiving station, showing the different paths of information transfer.


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Entangled States

Type II Spontaneous Parametric down-conversion

Non-linear optical process inside crystal Pulsed pump photons

Creation of two polarization entangled photons 2 & 3

Parametric down-conversion creating a signal and idler beam from the pump-

pulse. Energy and momentum conservation are shown on the right side.

Pump

p

kp

k(1)

k(2)

p= kp= k

(1)+ k

(2)

(2)

Ep

E1

E2

Ep= (2)

E1.E2*


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Experimental Realization UV pulse beam hits BBO crystal

twice

Photon 1 is prepared in initialstate

Photon 4 as trigger

Alice looks for coincidences

Bob knows that state isteleported and checks it.

Threefold coincidencef1f2d1(+45) in absence of f1f2d2(-45)

Temporal overlap betweenphoton 1,2

Experimental set-up for quantum teleportation, showing the UV pulsed beam that creates

the entangled pair, the beamsplitters and the polarisers.


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Outside Teleportation Region

For distinguishable photons, with p=0.5, 2photons end in different O/P ports

Photon 3 polarization undefined!

So, d1, d2 have 50% chances of receivingphoton 3

=> 25% probability for both f1f2d1 and

f1f2d2 threefold coincidences P(f1f2d1) = P(f1f2d2) = 0.25


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Inside Teleportation Region

Indistinguishable photons interfere!

Input state

Indistinguishable photons interfere!

Input state

If f1, f2 both click, then teleportation occurred and only d1f1f2coincidences should occur and d2f1f2 should be 0

Teleportation (d1f1f2 coincidences) achieved with 25% prob.


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Experimental Demonstration

Theoretical and experimental threefold coincidence detection between the two Bell state

detectors f1f2 and one of the detectors monitoring the teleported state. Teleportation is

complete when d1f1f2 (+45) is present in the absence of d2f1f2(-45) detection.


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Measured Coincidence Rates


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Summary

Deduced from the basic principles of quantum mechanics, it is possible totransfer the quantum state from one particle onto another over arbitrarydistances.

As an experimental elaboration of that scheme we discussed the teleportationof polarization states of photons.

But quantum teleportation is not restricted to that system at all. One couldimagine entangling photons with atoms or photons with ions, and so on.

Then teleportation would allow us to transfer the state of, for example, fastdecohering, short-lived particles onto some more stable systems.

This opens the possibility of quantum memories, where the information ofincoming photons could be stored on trapped ions, carefully shielded from theenvironment.

With this application we are in heart of quantum information processing.

Experimental Quantum Teleportation

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