3. Kvantna 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 pike kubiti na mreži (kvantni) fazni prehodi (5) povzetek

4. Entanglement: 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

5. Entanglement: quantum phenomenon

8. Primer uporabe prepletenosti: teleportacija

9. 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. Primer uporabe prepletenosti: teleportacija

10. R. Ursin et al., Nature 430, 849 (2004) Primer uporabe prepletenosti: teleportacija

12. A B Ψ original Ψ teleportacija

13. A B Ψ Ψ teleportacija

14. A B Ψ kopija Ψ Ψ original Ψ “NI kvantnega kloniranja” teleportacija

15. A B Meritev: kolaps (sesedenje?) stanja izvor parov EPR razdelitev skupnega para (singleta, npr.) Ψ Ψ naj bo teleportiran teleportacija

16. A B izvor parov EPR razdelitev skupnega para (singleta, npr.) teleportacija klasično pošlji izid meritve deluj z unitarnim operatorjem Ψ se pojavi Ψ Meritev: sesedenje stanja

17. 2 3 teleportacija

18. 2 3 teleportacija

19. 1,2 3 teleportacija 1.zavrti okoli x 2.zavrti okoli z 3.počivaj 4.zavrti okoli y “Bellova meritev” ?

20. 1,2 3 teleportacija

21. Quantifying entanglement: E A B two ‘spins’ in a pure state: Destillation of EPR pairs: Consider n such qubits pairs all in the state with E. Then by applying only local operations m singlet pairs can be extracted and E=m/n (for large n).

22. Quantifying entanglement: pure states A B two ‘spins’ in a pure state: “1” (or “2”) is also a pure state Entanglement measure E=1 E=0

23. A B Quantifying entanglement: mixed states special case: pure states

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

28. Example: Hubbard model (1D)

29. 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)

30. Concurrence: numerical examples A B References 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

31. Entanglement measure for two delocalized electrons

34. infinite-U Anderson model

35. Application: entanglement on demand

37. + Fullerene C 60, C 70, C 82, Sc@C 82, Ce@C 82, Nd@C 82 Sc 2 @C 80, Ce 2 @C 80, Er 3 N@C 80, Sc 3 N@C 80 Nanotubes (diameters 1.36nm and 1.49nm) Gas-Phase Nanotube Filling (300-500 o C): Reality …

38. Application: entanglement on demand (I)

39. Quasi 1D x

40. x T. Rejec and Y. Meir, Nature 2006

41. Application: entanglement on demand (I)

42. Application: entanglement on demand (II)

48. 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: double quantum dots

49. Thermal equilibrium A-B entanglement

50. Double quantum dots: entanglement versus the Kondo effect

51. Double quantum dots

52. Double quantum dot

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

56. Double quantum dots

57. spin-qubits charge-qubits

58. Double quantum dots

59. Zero magnetic field, thermal equilibrium A B

60. A B

61. A B

62. A B see also:

63. Zero magnetic field, thermal equilibrium A B see also:

64. Double quantum dots: entanglement versus the Kondo effect

65. Qubit arrays …

71. A B Povzetek

72. "Any sufficiently advanced technology is indistinguishable from magic." Arthur C. Clarke