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Quantum State Transferring through Spin Chains

Explore the efficient state transferring methods through spin chains at varying temperatures and dimension levels, highlighting the advantages of anti-ferromagnetic chains over ferromagnetic ones. Gain insights into entanglement distribution, average fidelity, and resistance to noise and temperature.

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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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