Experimental Quantum Teleportation Quantum systems for Information Technology Kambiz Behfar Phani Kumar.

Experimental Quantum Experimental Quantum TeleportationTeleportation

Quantum systems for Quantum systems for Information TechnologyInformation Technology

Kambiz BehfarKambiz BehfarPhani KumarPhani Kumar

ContentsContents

• Concept of Quantum TeleportationConcept of Quantum Teleportation IntroductionIntroduction

Quantum Teleportation CircuitQuantum Teleportation Circuit

Theoretical Results Theoretical Results

• Experimental RealizationExperimental Realization PrinciplesPrinciples

Entangled StatesEntangled States

Outside Teleportation RegionOutside Teleportation Region

Inside Teleportation RegionInside Teleportation Region

Measured Coincidence RateMeasured Coincidence Rate

SummarySummary

Quantum TeleportationQuantum Teleportation

Teleportation:

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

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

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

Quantum Teleportation Quantum Teleportation CircuitCircuit

( 0 1 1 0 ) / 2-Y = -

( ) ( )( ) ( )

( 0 1 1 0 ) 0 1 ( 0 1 1 0 ) 0 11

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

( 0 1 1 0 )

( 0 1 1 0 )1

( 0 0 11 )2

( 0 0 11 )

a b a by

a b a b

y

y

y

y

-é ù- Ä - - + + Ä - + +ê ú×Y =

- Ä + + + Ä -ê úë û

é - Ä - +ùê ú

+ Ä- +ê úê ú+ Ä +ê úê ú+ Äë û

Z

X

XZ

H

XM2 ZM1

y

-Y

M1

M2

0 1y a b= +

ProofProof

( )( )( )( )

( 0 0 11 ) / 2 ( 0 0 11 ) 1 0 0 0 1 0 0 0 11 1 1 1 0

( 0 0 11 ) / 2 ( 0 0 11 ) 1 0 0 0 1 0 0 0 11 1 1 1 0

( 0 1 1 0 ) / 2 ( 0 1 1 0 ) 0 1 0 1 0 0 11 1 0 0 1 0 1

( 0 1 1 0 ) / 2 ( 0 1 1 0 ) 0 1 0 1 0 0 11 1 0 0 1

Expand ing RH S

y a b a b a b

y a b a b a b

y a b a b a b

y a b a b a b

+ Ä = + Ä - = - + -

- Ä = - Ä + = + - -

+ Ä- = + Ä - + =- + + +

- Ä - = - Ä - - =- - - +

XZ

X

Z

0 1

0 0 1 1 1 0 0 1 0 1 0 1a b a b- - - - - - - - - - - - - - - - - - -

- - +

( 0 1 1 0 ) / 2 ( 0 1 1 0 ) / 2

( 0 0 11 ) / 2 ( 0 0 11 ) / 2

1( 0 1 ) ( 0 1 1 0 ) 0 0 1 1 1 0 0 1 0 1 0 1

2

Expand ing LH S

y y y y y

y a b a b a b

- - + - +

+ -

+ -

-

×Y =Y Ä- + Y Ä- + F Ä + F Ä

Y = + Y = -

F = + F = -

×Y = + × + = - - +

Z X XZ

QT Circuit

-Y

A complete Bell-state measurement can not only give the result that the two particles 1 and 2 are in the anti-symmetric state, but with equal probabilities of 25% we could find them 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 Bob applies

gate

Then Bob’s qubit is in

stateIf Alice obtains

10 b+a

01 b+a

10 b-a

01 b-a

10 b+a

-Y

+F

Theoretical Results

Principle of Quantum TeleportationPrinciple of Quantum Teleportation– Alice has particle 1Alice has particle 1

– Alice & Bob share EPR pair Alice & Bob share EPR pair

– Alice performs BSM Alice performs BSM causing entanglement causing entanglement between photon 1 and 2between photon 1 and 2

– Alice sends classical Alice sends classical information to Bobinformation to Bob

– Bob performs unitary Bob performs unitary transformationtransformation

– Teleporting the state not Teleporting the state not the particlethe particle

– Correlations used for data Correlations used for data transfertransfer

Schematic idea for quantum teleportation introducing Alice as a sending and Bob as a receiving station, showing the different paths of information transfer.

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*

Experimental RealizationExperimental Realization• UV pulse beam hits BBO UV pulse beam hits BBO

crystal twicecrystal twice

• Photon 1 is prepared in Photon 1 is prepared in initial stateinitial state

• Photon 4 as triggerPhoton 4 as trigger

• Alice looks for coincidencesAlice looks for coincidences

• Bob knows that state is Bob knows that state is teleported and checks it.teleported and checks it.

• Threefold coincidence Threefold coincidence ff11ff22dd11(+45°) in absence of (+45°) in absence of ff11ff22dd2 2 (-45°)(-45°)

• Temporal overlap between Temporal overlap between photon 1,2photon 1,2

Experimental set-up for quantum teleportation, showing the UV pulsed beam that creates the entangled pair, the beamsplitters and the polarisers.

Outside Teleportation RegionOutside Teleportation Region• For distinguishable photons, with For distinguishable photons, with p=0.5, 2 photons end in different O/P p=0.5, 2 photons end in different O/P portsports• Photon 3 polarization undefined!Photon 3 polarization undefined!• So, d1, d2 have 50% chances of So, d1, d2 have 50% chances of receiving photon 3receiving photon 3• => 25% probability for both f1f2d1 => 25% probability for both f1f2d1 and f1f2d2 threefold coincidences and f1f2d2 threefold coincidences • P(f1f2d1) = P(f1f2d2) = 0.25P(f1f2d1) = P(f1f2d2) = 0.25

Inside Teleportation RegionInside Teleportation Region– Indistinguishable photons Indistinguishable photons

interfere!interfere!– Input stateInput state

– Indistinguishable photons Indistinguishable photons interfere!interfere!

– Input stateInput state

– If f1, f2 both click, then teleportation occurred and only If f1, f2 both click, then teleportation occurred and only d1f1f2 coincidences should occur and d2f1f2 should be 0d1f1f2 coincidences should occur and d2f1f2 should be 0

– Teleportation (d1f1f2 coincidences) achieved with 25% Teleportation (d1f1f2 coincidences) achieved with 25% prob.prob.

Experimental Experimental DemonstrationDemonstration

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.

Measured Coincidence RatesMeasured Coincidence Rates

SummarySummary• Deduced from the basic principles of quantum mechanics, it is possible to

transfer the quantum state from one particle onto another over arbitrary distances.

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

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

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

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

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