Tailoring spin chain dynamics for fractional revivals
Department of Mathematics, Royal Holloway University of London, Egham, Surrey, TW20 0EX, UK
Published: | 2017-08-10, volume 1, page 24 |
Eprint: | arXiv:1609.01397v5 |
Doi: | https://doi.org/10.22331/q-2017-08-10-24 |
Citation: | Quantum 1, 24 (2017). |
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Abstract
The production of quantum states required for use in quantum protocols & technologies is studied by developing the tools to re-engineer a perfect state transfer spin chain so that a separable input excitation is output over multiple sites. We concentrate in particular on cases where the excitation is superposed over a small subset of the qubits on the spin chain, known as fractional revivals, demonstrating that spin chains are capable of producing a far greater range of fractional revivals than previously known, at high speed. We also provide a numerical technique for generating chains that produce arbitrary single-excitation states, such as the W state.
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[1] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt. Phys. Rev. Lett. 23, 880–884 (1969). 10.1103/PhysRevLett.23.880.
https://doi.org/10.1103/PhysRevLett.23.880
[2] A. K. Ekert. Phys. Rev. Lett. 67, 661–663 (1991). 10.1103/PhysRevLett.67.661.
https://doi.org/10.1103/PhysRevLett.67.661
[3] R. F. Werner. Phys. Rev. A 58, 1827–1832 (1998). 10.1103/PhysRevA.58.1827.
https://doi.org/10.1103/PhysRevA.58.1827
[4] A. Kay. Phys Rev A 79, 042330 (2009). 10.1103/PhysRevA.79.042330.
https://doi.org/10.1103/PhysRevA.79.042330
[5] V. Bužek and M. Hillery. Phys. Rev. A 54, 1844–1852 (1996). 10.1103/PhysRevA.54.1844.
https://doi.org/10.1103/PhysRevA.54.1844
[6] S. Pironio, et al. Nature 464, 1021–1024 (2010). 10.1038/nature09008.
https://doi.org/10.1038/nature09008
[7] R. Raussendorf and H. J. Briegel. Phys. Rev. Lett. 86, 5188 (2001). 10.1103/PhysRevLett.86.5188.
https://doi.org/10.1103/PhysRevLett.86.5188
[8] S. Bose. Phys. Rev. Lett. 91, 207901 (2003). 10.1103/PhysRevLett.91.207901.
https://doi.org/10.1103/PhysRevLett.91.207901
[9] M. Christandl, N. Datta, A. Ekert, and A. J. Landahl. Phys. Rev. Lett. 92, 187902 (2004). 10.1103/PhysRevLett.92.187902.
https://doi.org/10.1103/PhysRevLett.92.187902
[10] D. Burgarth and S. Bose. New J. Phys. 7, 135 (2005). 10.1088/1367-2630/7/1/135.
https://doi.org/10.1088/1367-2630/7/1/135
[11] M. Christandl, et al. Phys. Rev. A 71, 032312 (2005). 10.1103/PhysRevA.71.032312.
https://doi.org/10.1103/PhysRevA.71.032312
[12] A. Kay. Int J Quantum Inf. 8, 641 (2010). 10.1142/S0219749910006514.
https://doi.org/10.1142/S0219749910006514
[13] M.-H. Yung. Phys. Rev. A 74, 030303 (2006). 10.1103/PhysRevA.74.030303.
https://doi.org/10.1103/PhysRevA.74.030303
[14] P. Karbach and J. Stolze. Phys. Rev. A 72, 030301 (2005). 10.1103/PhysRevA.72.030301.
https://doi.org/10.1103/PhysRevA.72.030301
[15] H. L. Haselgrove. Phys Rev A 72, 062326 (2005). 10.1103/PhysRevA.72.062326.
https://doi.org/10.1103/PhysRevA.72.062326
[16] A. Wojcik, et al. Phys Rev A 72, 034303 (2005). 10.1103/PhysRevA.72.034303.
https://doi.org/10.1103/PhysRevA.72.034303
[17] S. R. Clark, C. M. Alves, and D. Jaksch. New J. Phys. 7, 124 (2005). ISSN 1367-2630. 10.1088/1367-2630/7/1/124.
https://doi.org/10.1088/1367-2630/7/1/124
[18] L. Dai, Y. P. Feng, and L. C. Kwek. J. Phys. A: Math. Theor. 43, 035302 (2010). ISSN 1751-8113. 10.1088/1751-8113/43/3/035302.
https://doi.org/10.1088/1751-8113/43/3/035302
[19] L. Banchi, E. Compagno, and S. Bose. Phys. Rev. A 91, 052323 (2015). 10.1103/PhysRevA.91.052323.
https://doi.org/10.1103/PhysRevA.91.052323
[20] V. X. Genest, L. Vinet, and A. Zhedanov. Annals of Physics 371, 348–367 (2016). 10.1016/j.aop.2016.05.009.
https://doi.org/10.1016/j.aop.2016.05.009
[21] A. Kay. New J Phys 19, 043019 (2017). 10.1088/1367-2630/aa68f9.
https://doi.org/10.1088/1367-2630/aa68f9
[22] A. Kay. Phys. Rev. Lett. 98, 010501 (2007). 10.1103/PhysRevLett.98.010501.
https://doi.org/10.1103/PhysRevLett.98.010501
[23] A. Marais, et al. New J. Phys. 15, 013038 (2013). ISSN 1367-2630. 10.1088/1367-2630/15/1/013038.
https://doi.org/10.1088/1367-2630/15/1/013038
[24] C. Godsil, S. Kirkland, S. Severini, and J. Smith. Phys. Rev. Lett. 109, 050502 (2012). 10.1103/PhysRevLett.109.050502.
https://doi.org/10.1103/PhysRevLett.109.050502
[25] E. Jonckheere, F. C. Langbein, and S. G. Schirmer. Quantum Inf Process 14, 4751–4785 (2015). ISSN 1570-0755, 1573-1332. 10.1007/s11128-015-1136-4.
https://doi.org/10.1007/s11128-015-1136-4
[26] G. M. L. Gladwell, editor. Inverse Problems in Vibration, volume 119 of Solid Mechanics and Its Applications. Kluwer, Dordrecht, (2005). ISBN 978-1-4020-2670-6. 10.1007/1-4020-2721-4.
https://doi.org/10.1007/1-4020-2721-4
[27] C. Albanese, M. Christandl, N. Datta, and A. Ekert. Phys. Rev. Lett. 93, 230502 (2004). 10.1103/PhysRevLett.93.230502.
https://doi.org/10.1103/PhysRevLett.93.230502
[28] M. B. Plenio, J. Hartley, and J. Eisert. New J. Phys. 6, 36–36 (2004). 10.1088/1367-2630/6/1/036.
https://doi.org/10.1088/1367-2630/6/1/036
[29] A. Kay and M. Ericsson. New J. Phys. 7, 143–143 (2005). 10.1088/1367-2630/7/1/143.
https://doi.org/10.1088/1367-2630/7/1/143
[30] S. Bravyi, M. B. Hastings, and F. Verstraete. Phys. Rev. Lett. 97, 050401 (2006). 10.1103/PhysRevLett.97.050401.
https://doi.org/10.1103/PhysRevLett.97.050401
[31] M. Murphy, S. Montangero, V. Giovannetti, and T. Calarco. Phys. Rev. A 82, 022318 (2010). 10.1103/PhysRevA.82.022318.
https://doi.org/10.1103/PhysRevA.82.022318
[32] A. Kay. Perfect Revivals on Spin Chains. https://figshare.com/articles/Perfect_Revivals_on_Spin_Chains/4110033, (2016). 10.6084/m9.figshare.4110033.v1.
https://doi.org/10.6084/m9.figshare.4110033.v1
https://figshare.com/articles/Perfect_Revivals_on_Spin_Chains/4110033
[33] A. Perez-Leija, et al. Phys. Rev. A 87, 012309 (2013). 10.1103/PhysRevA.87.012309.
https://doi.org/10.1103/PhysRevA.87.012309
[34] S. Weimann, et al. Opt Lett 39, 123 (2014). ISSN 0146-9592, 1539-4794. 10.1364/OL.39.000123.
https://doi.org/10.1364/OL.39.000123
[35] R. J. Chapman, et al. Nat Commun 7, 11339 (2016). 10.1038/ncomms11339.
https://doi.org/10.1038/ncomms11339
[36] M. Gräfe, et al. Nat. Photon. 8, 791–795 (2014). 10.1038/nphoton.2014.204.
https://doi.org/10.1038/nphoton.2014.204
[37] A. Kay. Phys. Rev. A 84, 022337 (2011). 10.1103/PhysRevA.84.022337.
https://doi.org/10.1103/PhysRevA.84.022337
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[1] Alastair Kay, "Coprocessors for quantum devices", Physical Review A 97 3, 032316 (2018).
[2] Alastair Kay, "Perfect coding for dephased quantum state transfer", Physical Review A 97 3, 032317 (2018).
[3] Tony J. G. Apollaro, Guilherme M. A. Almeida, Salvatore Lorenzo, Alessandro Ferraro, and Simone Paganelli, "Spin chains for two-qubit teleportation", Physical Review A 100 5, 052308 (2019).
[4] Gabriel Coutinho, Luc Vinet, Hanmeng Zhan, and Alexei Zhedanov, "Perfect state transfer in a spin chain without mirror symmetry", Journal of Physics A: Mathematical and Theoretical 52 45, 455302 (2019).
[5] Catherine Keele and Alastair Kay, "Noise-reducing encoding strategies for spin chains", Physical Review A 105 3, 032613 (2022).
[6] Éric-Olivier Bossé and Luc Vinet, "Coherent Transport in Photonic Lattices: A Survey of Recent Analytic Results", SIGMA 13, 074 (2017).
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