07.06.2006 Uni-Heidelberg Physikalisches Insitut Jian-Wei Pan Multi-Particle Entanglement & It’s...

07.06.2006 Uni-Heidelberg

Physikalisches Insitut

Jian-Wei Pan

Multi-Particle Entanglement & It’s Application in Quantum Networks

Jian-Wei Pan

Lecture Note 5



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Polarization Entangled Photons

212112

212112

||||2

1|

||||2

1|

HVVH

VVHH

[P. G. Kwiat et al., Phys. Rev. Lett. 75, 4337 (1995).]



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Post Selection

1 2

2' 1' 1' 2'

1' 2' 1' 2' 1' 2'

H V H V

H iV H iV

H H V V i VH HV

1' 2' 1' 2'H H V V



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3-Photon

)()(2

1 ''''babababa HVVHHVVH

Initial State:

Four-fold coincidence

1 2 3 1 2 3T TH H H V or H VV H

)(2

1321321 HVVVHHHT

Final State:



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Bell’s Inequality and Violation of Local Realism

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

Bell’s inequality states that certain statistical correlations predicted by QM for measurements on two-particle ensembles cannotbe understood within a realistic picture based on local properties of each individual particle.

LR prediction: 2MAXS 22MAXSQM prediction:

An unstatisfactory feature!

In the derivation of BI such a local realistic and thus classical picture can explain perfect correlations and is only in conflict with statistical prediction of quantum mechanics.



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conflict with local realism

123 1 2 3 1 2 3

Consider a three-photon GHZ state written in basis

1

2

z

H H H V V V

1: ' ,

21

' .2

x H H V

V H V

1: ,

21

.2

y R H i V

L H i V

Linear polarizatoin basis

circular polarization basis

z

1 0, denotes the eigenstate of respectively

0 1H V



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' ' ' '1 2 3 123 1 2 3 1 2 3 1 2 3 1 2 3

' ' ' '1 2 3 123 1 2 3 1 2 3 1 2 3 1 2 3

' ' ' '1 2 3 123 1 2 3 1 2 3 1 2 3 1 2 3

1:

21

:21

:2

y y x

y x y

x y y

R L H L R H R R V L L V

R H L L H R RV R LV L

H R L H L R V R R V L L

123

1 2 3 1 2 3 1 2 3

therefore state is the eigenstate of operators

with value -1y y x y x y x y y

、、




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EPR reality criterion: the individual value of any local operator is predetermined. There exists an element of local reality Six corresponding to operator 1,2,3 .ix i


All six of the elements of reality Six and Siy have to be there, each with the values +1 and –1! 1 2 3

1 2 3

1 2 3

1,

1,

1.

y y x

y x y

x y y

S S S

S S S

S S S



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What outcomes are possible?

Consider measurement of 45° linear polarization basis

2 2 21 2 3 1 1 2 2 3 3

1 2 3 1 2 3 1 2 3

( ) ( ) ( )

( )( )( )

1

x x x x y x y x y

x y y y x y y y y

S S S S S S S S S

S S S S S S S S S

local realism

' ' ' ' ' ' ' ' ' ' ' '1 2 3 1 2 3 1 2 3 1 2 3, , ,V V V H H V H V H V H H

Possible outcomes:



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What outcomes are possible?

quantum physics

' ' ' ' ' ' ' ' ' ' ' '123 1 2 3 1 2 3 1 2 3 1 2 3

1

2H H H H V V V H V V V H

1 2 3 !1x x xS S S

Whenever local realism predicts a specific result definitely to occur for a measurement for one of the photons based on the results for the other two, quantum physics definitely predicts the opposite result!

' ' ' ' ' ' ' ' ' ' ' '1 2 3 1 2 3 1 2 3 1 2 3, , ,H H H H V V V H V V V H

Possible outcomes:



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Experimental Results

J.-W. Pan et al., Nature (London) 403, 515 (2000)



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An improved 3- & 4-photon source

12 34

1 2 1 2 3 4 3 4

1 2 3 4 1 2 3 4

4 4 1 2 3 1 2 3

1

21

2

H H V V H H V V

H H H H V V V V

H V H H H V V V

[J.-W. Pan et al., Rev. Lett. 86, 4435 (2001) ]



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• Quantum secret sharing A procedure for splitting a message into several parts so that no subset of parts is sufficient to read the message, but the entire set is. [M. Hillery et al., Phys. Rev. A 59, 1829 (1999).]

• Third-Man Quantum CryptographyA procedure that the third man, a controller, can control whether the users, say Alice and Bob, can communicate in a secure way while he has no access whatsoever on the content of the communication between Alice and Bob. [M. Żukowski et al., Acta Phys. Pol. 93, 187 (1998).]

Advanced Quantum Cryptography



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Schemes for QSS and TQC

1

2abc a b c a b cH H H V V V

ViHy

VHx

2

1

,2

1

A xxx measurement

1

2 a b a b cabc

a b a b c

x x x x x

x x x x x



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Quantum Secret Sharing

1

2 21

2 21

2 21

2 2

a b a b c a b a b c

a b a b c a b a b c

a b a b c a b a b c

a b a b c a b a b c

x x x x x x x x x x

y y y y x y y y y x

y x y x y y x y x y

x y x y y x y x y y

xxx, xyy, yxy, yyx

xyx, yxx, xxy, xyx



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Setup

[Z. Zhao et al., Phy. Rev. Lett. 91 180401 (2003).

A ultra-stable high intensity source:

2 four-fold coincidence per second!

100 times brighter!stable for a few months!



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Result for QSS

From 327 579 bits of raw key with a QBER of 12.9%, after security check and error reduction, Alice and Bob jointly generate 87 666 bits cured key with Charlie with a QBER of 0.3%.



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Third-Man’s Control

• If all of them randomly select the base to measure the polarization. Any two of them can create a coding by being told the other one’s measurement result.

• If Charlie rejects to tell them his selection or just does not make any selection then Alice and Bob can get nothing useful for the cryptography.



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Result for TQC

With the permission of Charlie, after security check and error reduction Alice can generate a 87 666 bits cured key with Bob, with the same QBER. Otherwise, Without knowing Charlie's results, the only thing Alice and Bob can do is to randomly guess Charlie's results and continue the same encoding and error reduction procedure. In our experiment, after performing twice error reductions, the QBER remains 49.999%.

[Y.-A. Chen et al., Phy. Rev. Lett. 95, 200502 (2005) ]



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conflict with local realism in 4-photon case

x x x x x y x y x x y y , , xyyx

y y y y y x y x y y x x , , yxxy

1 1' '

2 21 1

2 2

x

y

H H V V H V

R H i V L H i V

: 、

: 、

1 2 3 4 1 2 3 4

1

2H V V H V H H V

1' ' ' ' ' ' ' '

2 2

' ' ' ' ' ' ' '

' ' ' ' ' ' ' '

' ' ' ' ' ' ' '

H H H H H H V V

H V H V H V V H

V H H V V H V H

V V H H V V V V

:x x x x



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Violation of Local Realism

[Z. Zhao et al., Phy. Rev. Lett. 91 180401 (2003).



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A new protocol for 3-Photon

[J. G. Rarity and P. R. Tapster,

Phys. Rev. A 59, R35 (1999).]

1 1 23 23H V HH VV

123 123HHH VVV



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5-Photon

4545232311

VVHHVVHHVH

Five-fold Coincidence:

1234512345

VVVVVHHHHH



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Encoding operation for simple quantum error

correction 12345 1 2345

12 3 4 5 3 4 5

12 3 4 5 3 4 5

12 3 4 5 3 4 5

12 3 4 5 3 4 5

| | |

1[| ( | | | | | | )

2| ( | | | | | | )

| ( | | | | | | )

| ( | | | | | | )]

H H H V V V

H H H V V V

V V V H H H

V V V H H H

This implies that a joint Bell measurement on photons 1 and 2

would project the state of photons 3, 4 and 5 into one of the four

corresponding states, which can be used for either one bit-flip

error or phase-shift error correction in quantum communication.



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Quantum State Sharing &Open-destination

Teleportation

345345

11

VVVHHH

VH

If we perform a +45-degree measurement on photons 4 and 5, then photon 3 is left in the state of photon 1.

In a similar manner the initial state of photon 1 can also be teleported either onto photon 4 or photon 5.

[A. Karlsson, et al., Phys. Rev. A 58, 4394 (1998) ]



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Further Demonstration • In contrast to the original teleportation scheme, after the encoding

operation the destination of teleportation is left open until we perform a polarization measurement on two of the remaining three photons.

• Even though photons 3, 4 and 5 are far away from each other, one can still choose which particle should act as the output where the initial state of photon 1 is transferred to. This is why we have called the encoding-decoding procedure as open-destination teleportation.

• It is therefore a generalization of standard teleportation, when no prior agreement on the final destination of the teleportation is necessary.

• It is also a generalization of Quantum State Sharing. No subset of parts is sufficient to decode the state, but the entire set is. It broadens the scope of quantum information networks allowing quantum communication between multiple nodes, while providing security against malicious parties in the network as well as node and channel failures.



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Setup for Five-photon GHZ Entanglement

[Z. Zhao et al., Nature 430, 54 (2004). ]



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CNOT operation for two-independent photons

+/-?

H/V?

1

2

2 34 5

PBST( ); R( ) 2 3 4 2 3 4 5 5

PBST( ); R( ) 2 3 2 3 4 4 5 5

2 3 2 3 4 4 5 5

Conditional 3 at H+VConditional 4 at H

H V

H V H V

H V HV VH H V

HH V VV H H V

HH VV H V H V

HH VV H V H V

2 5 5 2 5 5H V H V H V



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Control Target Control’ Target’

H H H V

H V H H

V H V H

V V V V

CNOT Gate

[T. B. Pittman, PRA 64,062311(2001)]

[S. Gasparoni et al., Phys. Rev. Lett. 93, 020504 (2004); Z. Zhao et al., Phys. Rev. Lett. 94, 0304501 (2005).]

A full Bell state Measurement for 100% Teleportation



Jian-Wei Pan

Most recently... 6-Photon

[Q. Zhang et al., In preparation for Science ]

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