Kvantna prepletenost v nano sistemih

3. Kvantna prepletenost v nano sistemih • motivacija • definicija kvantne prepletenosti • statični in leteči kvantni biti • prepletenost na zahtevo • 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. Primer uporabe prepletenosti: teleportacija • 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.

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

11. Primer uporabe prepletenosti: teleportacija

12. teleportacija A B Ψ original Ψ

13. teleportacija A B Ψ Ψ original Ψ

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

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

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

17. teleportacija 2 3

18. teleportacija 2 3

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

20. teleportacija 1,2 3

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

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

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

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

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

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

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

32. Entanglement measure for two delocalized electrons

33. Entanglement measure for two delocalized electrons

34. Entanglement measure for two delocalized electrons infinite-U Anderson model

35. Application: entanglement on demand

37. Reality … Gas-Phase Nanotube Filling (300-500oC): + Fullerene C60, C70, C82, Sc@C82, Ce@C82, Nd@C82 Sc2@C80, Ce2@C80, Er3N@C80, Sc3N@C80 Nanotubes (diameters 1.36nm and 1.49nm)

38. Application: entanglement on demand (I)

39. Quasi 1D x

40. Quasi 1D x T. Rejec and Y. Meir, Nature 2006

41. Application: entanglement on demand (I)

42. Application: entanglement on demand (II)

43. Application: entanglement on demand (II)

44. Application: entanglement on demand (II)

45. Application: entanglement on demand (II)

46. Application: entanglement on demand (II)

47. Application: entanglement on demand (II)

48. Chan et al, Nanotechnology 15, 609 (2004) Vidan et al, Applied Phys. Lett. 85, 3602 (2004) Elzerman et al, PRB 67, 16308 (2003) QD QD Electrostatic gates Realistic qubit pairs: double quantum dots

49. Thermal equilibrium A-B entanglement

50. Double quantum dots: entanglement versus the Kondo effect