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Quantum State Transferring through Spin Chains

Quantum State Transferring through Spin Chains. Abolfazl Bayat Sharif University of Technology Tehran, Iran. IICQI September 2007 Kish Island, Iran. Topics. Introduction State transferring via natural evolution Nonzero temperature d-level systems Anti ferromagnetic spin chains

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Quantum State Transferring through Spin Chains

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  1. Quantum State Transferring through Spin Chains Abolfazl BayatSharif 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 Maximally Entangled Time Passing Length S. Bose, PRL (2003)

  7. Non zero temperature 1 2 3 N-1 N Basis for sites 1,2,…,N-1

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

  9. Entanglement distribution Maximally Entangled 0’ 0 1 N-1 N Ferromagnetic Anti Ferromagnetic KT KT E E time time 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 A. Bayat, V. Karimipour , PRA (2005)

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

  14. Anti ferromagnetic chain 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). 2- Because of SU(2) symmetry in Hamiltonian and also in ground state the channel is a depolarizing channel

  15. Entanglement distribution 0’ 0 1 N-1 N Time Passing Ferromagnetic Anti ferromagnetic In anti ferromagnetic chains entanglement rises from zero with divergent gradient

  16. First Maximum time Length Entanglement Length Purity Length 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

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

  18. Markovian decoherence E0 EN E0’ 0’ 0 1 N-1 N Anti ferromagnetic Ferromagnetic Entanglement Anti ferromagnetic chain decays slower than ferromagnetic one

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

  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.

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