Tailoring spin chain dynamics for fractional revivals

Alastair Kay

doi:10.22331/q-2017-08-10-24

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).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

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.

Featured image: A spin chain can be engineered so that an excitation, injected onto a single site of the chain, evolves into a specified superposition of sites, as time flows from top to bottom, making use of intricate interference patterns.

► BibTeX data

@article{Kay2017tailoringspinchain,
  doi = {10.22331/q-2017-08-10-24},
  url = {https://doi.org/10.22331/q-2017-08-10-24},
  title = {Tailoring spin chain dynamics for fractional revivals},
  author = {Kay, Alastair},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {1},
  pages = {24},
  month = aug,
  year = {2017}
}

► References

[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

Cited by

[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).

The above citations are from Crossref's cited-by service (last updated successfully 2024-08-24 07:22:10) and SAO/NASA ADS (last updated successfully 2024-08-24 07:22:11). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.