Abstract
We analytically investigate the one-excitation spin dynamics in a homogeneous closed spin-1/2 chain via diagonalization of the one-excitation block of the XX-Hamiltonian, which allows to derive the analytical expressions for probability amplitudes describing state transfers between any two spins of a chain. We analytically investigate the M-neighbor approximation (\(M\ge 1\)) of spin dynamics with arbitrary initial state and analyze its accuracy using special integral characteristics defined in terms of the above probability amplitudes. We find M providing the required accuracy of evolution approximation for chains of different lengths.
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References
Bose, S.: Quantum communication through an unmodulated spin chain. Phys. Rev. Lett. 91, 207901 (2003)
Christandl, M., Datta, N., Ekert, A., Landahl, A.J.: Perfect state transfer in quantum spin networks. Phys. Rev. Lett. 92, 187902 (2004)
Karbach, P., Stolze, J.: Spin chains as perfect quantum state mirrors. Phys. Rev. A 72, 030301(R) (2005)
Gualdi, G., Kostak, V., Marzoli, I., Tombesi, P.: Perfect state transfer in long-range interacting spin chains. Phys. Rev. A 78, 022325 (2008)
Jourdan, P., Wigner, E.: Uber das paulische äquivalenzverbot. Z. Phys. 47 (9), 631 (1928)
Cruz, H.B., Goncalves, L.L.: Time-dependent correlations of the one-dimensional isotropic XY model. J. Phys. C: Solid State Phys. 14, 2785 (1981)
Abragam, A.: The Principles of Nuclear Magnetism. Clarendon Press, Oxford (1961)
Davis, Ph.J.: Circulant Matrices. Wiley, New York (1970)
Gray, R.M.: Toeplitz and circulant matrices: a review. Found. Trends Commun. Inf. Theory 2(3), 155–239 (2006)
Engelsberg, V., Lowe, I.J., Carolan, J.I.: Nuclear-magnetic-resonance line shape of a linear chain of spins. Phys. Rev. B 7, 924 (1973)
Bochkin, G.A., Fel’dman, E.B., Vasil’ev, S.G.: The exact solution for the free induction decay in a quasi-one-dimensional system in a multi-pulse NMR experiment. Phys. Lett. A 383, 2993 (2019)
Doronin, S.I., Maximov, I.I., Fel’dman, E.B.: Multiple-quantum dynamics of one-dimensional nuclear spin systems in solids. J. Exp. Theor. Phys. 91(3), 597 (2000)
Cappellaro, P., Ramanathan, C., Cory, D.G.: Simulations of information transport in spin chains. Phys. Rev. Lett. 99, 250506 (2007)
Koh, C.Y., Kwek, L.C., Wang, S.T., Chong, Y.Q.: Entanglement and discord in spin glass. Laser Phys. 23(2), 025202 (2013)
Ye, B.-L., Li, B., Li-Jost, X., Fei, Sh.-M.: Quantum correlations in critical XXZ system and LMG model. Int. J. Quant. Inf. 16, 1850029 (2018)
Zenchuk, A.I.: Remote creation of a one-qubit mixed state through a short homogeneous spin-1/2 chain. Phys. Rev. A 90, 052302(13) (2014)
Zwick, A., Álvarez, G.A., Stolze, J., Osenda, O.: Robustness of spin-coupling distributions for perfect quantum state transfer. Phys. Rev. A 84, 022311 (2011)
Zwick, A., Álvarez, G.A., Stolze, J., Osenda, O.: Spin chains for robust state transfer: modified boundary couplings versus completely engineered chains. Phys. Rev. A 85, 012318 (2012)
Zwick, A., Álvarez, G.A., Stolze, J., Osenda, O.: Quantum state transfer in disordered spin chains: How much engineering is reasonable? Quant. Inf. Comput. 15(7–8), 582 (2015)
Yosida, K.: Theory of Magnetism. Springer (1996)
Landau, L.D., Lifshitz, E.M.: Quantum Nechanics. Non-relativistic Theory. Course of Theoretical Physics, vol. 3. Pergamon, New York (1977)
Cappellaro, P., Ramanathan, C., Cory, D.G.: Dynamics and control of a quasi-one- dimensional spin system. Phys. Rev. A 76, 032317 (2007)
Fel’dman, E.B., Zenchuk, A.I.: \(M\)-neighbor approximation in one-qubit state transfer along zigzag and alternating spin-1/2 chains. Phys. Scr. 97(9), 095101 (2022)
Fel’dman, E.B., Zenchuk, A.I.: Nearest-neighbor approximation in one-excitation state evolution along spin-1/2 chain governed by \(XX\)-Hamiltonian. Phys. Lett. A 457, 128572 (2023)
Doronin, S.I., Fel’dman, E.B., Guinzbourg, I.. Ya.., Maximov, I.I.: Supercomputer analysis of one-dimensional multiple-quantum dynamics of nuclear spins in solids. Chem. Phys. Lett. 341, 144 (2001)
Dobrovitski, V.V., De Raedt, H.A., Katsnelson, M.I., Harmon, B.N.: Quantum oscillations without quantum coherence. Phys. Rev. Lett. 90, 210401 (2003)
Zhang, W.X., Cappellaro, P., Amtler, N., Pepper, B., Cory, D.G., Dobrovitski, V.V., Ramanathan, C., Viola, L.: NMR multiple quantum coherences in quasi-one-dimensional spin systems: comparison with ideal spin-chain dynamics. Phys. Rev. A 80, 052323 (2009)
Álvarez, G.A., Danieli, E.P., Levstein, P.R., Pastawski, H.M.: Quantum parallelism as a tool for ensemble spin dynamics calculations. Phys. Rev. Lett. 101, 120503 (2008)
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We acknowledge funding from the Ministry of Science and Higher Education of the Russian Federation (Grant No. 075-15-2020-779).
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Fel’dman, E.B., Kuznetsova, E.I. & Zenchuk, A.I. One-excitation spin dynamics in homogeneous closed chain governed by XX-Hamiltonian. Quantum Inf Process 23, 39 (2024). https://doi.org/10.1007/s11128-023-04250-4
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DOI: https://doi.org/10.1007/s11128-023-04250-4