1. Quantum State Transferring through Spin Chains Abolfazl Bayat Sharif University of Technology Tehran, Iran. IICQI September 2007 Kish Island, Iran.

2. Topics Introduction State transferring via natural evolution Nonzero temperature d-level systems Anti ferromagnetic spin chains Conclusion

3. Short Distance communication

4. Perfect state transferring Sequential of swap operators perform the perfect transferring but it needs a high control on each state

5. Natural time evolution Time Passing

6. Entanglement Distribution Time Passing Maximally Entangled S. Bose, PRL (2003) Length

7. Non zero temperature 123N-1N Basis for sites 1,2,…,N-1

8. Average fidelity 1- The average fidelity decreases when the temperature increases 2- The optimal time is independent of the temperature KT time

9. Entanglement distribution Maximally Entangled 0’01N-1N A. Bayat, V. Karimipour, PRA (2005) FerromagneticAnti Ferromagnetic 1- Entanglement decays when the temperature increases 2- For ferromagnetic chains non analyticity is appeared when the temperature is increased but in anti ferromagnetic chains even in zero temperature we have non analyticity E KT time E KT

10. d Level states Preparing the spin chains with dimension higher than two is easier in laboratory C.F. Hirjibehedin, et.al., Science (2006) and A J. Heinrich, et.al., Science (2004).

11. Random Swapping Hamiltonian Spin 1/2 Spin 1

12. Average fidelity r-s=4 r-s=7 r-s=14 d 1- Average fidelity decreases by increasing the dimension and saturates to some specific value 2- Perfect transferring is possible for a chain of length four in any dimension

13. Entanglement distribution A. Bayat, V. Karimipour, PRA (2007) d=2 d=3 d=4 time E Entanglement distribution is better for higher dimensions

14. Anti ferromagnetic chain 2- Because of SU(2) symmetry in Hamiltonian and also in ground state the channel is a depolarizing channel 1- In laboratory anti ferromagnetic spin chains can be prepared easier than ferromagnetic one C.F. Hirjibehedin, et.al., Science (2006) A J. Heinrich, et.al., Science (2004).

15. Entanglement distribution Time Passing0’01N-1N Ferromagnetic Anti ferromagnetic In anti ferromagnetic chains entanglement rises from zero with divergent gradient

16. First Maximum 1-AFM chains transfer the entanglement faster 2-The amount of entanglement and purity that can be gained is much more higher in Anti ferromagnetic chains time Entanglement Purity Length

17. Non Zero temperature 0’01N-1N Entanglement KT Anti ferromagnetic Ferromagnetic Enatnglemnet decays with increasing the temperature but Anti ferromagnetic chain is more resistive to the temperature

18. Markovian decoherence 0’01N-1N E 0’ E0E0 ENEN Anti ferromagnetic chain decays slower than ferromagnetic one Entanglement Anti ferromagnetic Ferromagnetic

19. Entanglement propagation inside the chain In a chains with even number of spins there is no entanglement between site 0’ and odd sites during the time evolution Jt 0’01N-1N

20. Conclusion Average fidelity and entanglement decay by increasing the temperature but the optimal time is almost independent of temperature and Noise. In ferromagnetic chain non analytic treatment is created in high temperatures but in anti ferromagnetic chains non analyticity is exist in any temperature. Average fidelity is decreased by increasing the dimension of the states but entanglement distribution is improved.. Anti ferromagnetic chain is faster for communication and has a better resistance against temperature and noise than a ferromagnetic chain.