kvantna prepletenost v nano sistemih (1) motivacija (2) definicija kvantne prepletenosti (3)...

Kvantna prepletenost v nano sistemihKvantna prepletenost v nano sistemih

(1) motivacija (2) definicija kvantne prepletenosti(3) statični in leteči kvantni biti(4) prepletenost na zahtevo(5) stabilnost in sesedenje prepletenosti:

dvojne kvantne pikekubiti na mreži(kvantni) fazni prehodi

(5) povzetek

Entanglement: quantum phenomenonEntanglement: quantum phenomenon

"When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.“ Arthur C. Clarke

Entanglement: quantum phenomenonEntanglement: quantum phenomenon

Primer uporabe prepletenostiPrimer uporabe prepletenosti: : teleportacijateleportacija

• D. Bouwmeester et al. Experimental quantum teleportation. Nature, page 575, 1997.

• Y. Kim et al. Quantum teleportation of a polarization state with a complete bell state measurement. Physical Review Letters, page 1370, 2000.

• I. Marcikic et al. Long-distance teleportation of qubits at telecommunication wavelengths. Nature, page 509, 2003.

• R. Ursin et al. Quantum teleportation across the Danube. Nature, page 849, 2004.


R. Ursin et al., Nature 430, 849 (2004)


A B

Ψ

original Ψ

teleportacijateleportacija

A B

Ψ

original Ψ

Ψ


A B

Ψ

kopija Ψ

Ψ

original Ψ

“NI kvantnega kloniranja”


http://upload.wikimedia.org/wikipedia/en/5/5f/Dolly_the_sheep2-thumb.jpg

A B

Meritev: kolaps (sesedenje?) stanja

izvor parov EPR

razdelitev skupnega para (singleta, npr.)

Ψ

Ψ naj bo teleportiran


A B

izvor parov EPR

razdelitev skupnega para (singleta, npr.)


klasično pošlji izid meritve

deluj z unitarnim operatorjem

Ψ se pojavi

Ψ

Meritev: sesedenje stanja

2 3


1,2 3


1. zavrti okoli x2. zavrti okoli z3. počivaj4. zavrti okoli y

“Bellova meritev”

?

1,2 3


Quantifying entanglement: Quantifying entanglement: EE

A B two ‘spins’ in a pure state:

Destillation of EPR pairs:

Consider n such qubits pairs all in the state with E. Then byapplying only local operations m singlet pairs can be extracted and E=m/n (for large n).

E

Quantifying entanglement: pure statesQuantifying entanglement: pure states

A Btwo ‘spins’ in a pure state:

“1” (or “2”) is also a pure state

Entanglement measure

E=1

E=0

A B

Quantifying entanglement: mixed statesQuantifying entanglement: mixed states

AB

( )E f C special case: pure states

Entanglement measure for two d e l o c a l i s e d electrons


A. Ramšak, I. Sega, and J.H. Jefferson PRA 74, 010304(R) (2006)

Concurrence: numerical examples

A BReferences

•A. R., I. Sega, and J.H. Jefferson, Phys. Rev. A 74, 010304(R) (2006).

• A. R., J. Mravlje, R. Žitko, and J. Bonča, Phys. Rev. B 74, 241305(R) (2006).

•G. Giavaras, J.H. Jefferson, A. R., T.P. Spiller, and C. Lambert, Phys. Rev. B 74, 195341 (2006).

•J. Mravlje, A. R., and T. Rejec, Phys. Rev. B 73, 241305(R) (2006).

•D. Gunlycke, J.H. Jefferson, T. Rejec, A. R., D.G. Pettifor, and G.A.D. Briggs, J. Phys.: Condens. Matter 18, S851 (2006).

•J.H. Jefferson, A. R., and T. Rejec, Europhys. Lett. 75, 764 (2006).

•S. El Shawish, A. R., and J. Bonča, Phys. Rev. B 75, 205442 (2007).

•A. R. and J. Mravlje, cond-mat/0701363. •M. Habgood, J.H. Jefferson, A. R., D.G. Pettifor,

and G.A.D. Briggs, subm. to Phys. Rev. B

Entanglement measure for two delocalized electronsEntanglement measure for two delocalized electrons

Entanglement measure for two delocalized electronsEntanglement measure for two delocalized electrons

infinite-U Anderson model

ApplicationApplication: entanglement on demand: entanglement on demand

E:\presentations\04QIP\qlg-4b.exe

+

FullereneC60, C70, C82, Sc@C82, Ce@C82, Nd@C82

Sc2@C80, Ce2@C80, Er3N@C80, Sc3N@C80

Nanotubes

(diameters 1.36nm and 1.49nm)

Gas-Phase Nanotube Filling (300-500oC):

Reality …Reality …

ApplicationApplication: entanglement on demand (I): entanglement on demand (I)

Quasi 1DQuasi 1D

x

Quasi 1DQuasi 1D

x

T. Rejec and Y. Meir, Nature 2006

ApplicationApplication: entanglement on demand (I): entanglement on demand (I)

ApplicationApplication: entanglement on demand (II): entanglement on demand (II)

Chan et al, Nanotechnology 15, 609 (2004)

Vidan et al, Applied Phys. Lett. 85, 3602 (2004)

Electrostatic gates

QD

Elzerman et al, PRB 67, 16308 (2003)

QD

Realistic qubit pairs: dRealistic qubit pairs: double quantum dotsouble quantum dots

Thermal equilibrium A-B entanglement

/B J/T J

2

4t

JU

C

., .B const T const

Double quantum dots: entanglement versus the Kondo effect

2ABn

Double quantum dots

Double quantum dotDouble quantum dot

2d t

2(b)

0

t U

V

2(a) t U

212

K(c) 4 2t

J TU

2 12t t t''

2RKKY KJ T

Double quantum dotDouble quantum dot

2d t

2(b)

0

t U

V

2(a) t U

212

K(c) 4t

J TU

2 12t t t''

2(d) 0 & ~ : (4) Kondot V U SU

2d t

2(b)

0

t U

V

2(a) t U

212

K(c) 4t

J TU

2(d) 0 & ~ : (4) Kondot V U SU

J. Mravlje, A. Ramšak, and T. Rejec, Phys. Rev. B 73, 241305(R) (2006)

Also for finite hibridization: [ (4)] ~ [ (2)]K KT SU U T SU

half filling: 2n

Double quantum dots

Double quantum dots

spin-qubits

charge-qubits

Double quantum dots

2

4t

JU

Zero magnetic field, thermal equilibrium

A

B

0, .B T const

2

4t

JU

/J U


A

B

/J U


2 cJ

A

B

see also:

/J U


3 ~cJ

A

B

see also:

Double quantum dots: entanglement versus the Kondo effect

Qubit arrays …Qubit arrays …

A B

PovzetekPovzetek

"Any sufficiently advanced technology is indistinguishable from magic."

Arthur C. Clarke

kvantna prepletenost v nano sistemih (1) motivacija (2) definicija kvantne prepletenosti (3)...

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