Abstract
Ballistic quantum information transfer through spin chains is based on the idea of making the spin dynamics ruled by collective excitations with linear dispersion relation. Unlike perfect state transfer schemes, a ballistic transmission requires only a minimal engineering of the interactions; in fact, for most practical purposes, the optimization of the couplings to the ends of the chain is sufficient to obtain an almost perfect transmission. In this work we review different ballistic quantum state transfer protocols based on the dynamics of quasi-free spin chains, and further generalize them both at zero and finite temperature. In particular, besides presenting novel analytical results for XX, XY, and Ising spin models, it is shown how, via a complete control on the first and last two qubits of the chain, destructive thermal effects can be cancelled, leading to a high-quality state transmission irrespective of the temperature.
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References
D. Press, T.D. Ladd, B. Zhang, Y. Yamamoto, Nature 456, 218 (2008)
C. Weitenberg, M. Endres, J. Sherson, M. Cheneau, P. Schauß, T. Fukuhara, I. Bloch, S. Kuhr, Nature 471, 319 (2011)
I. Chiorescu, Y. Nakamura, C.M. Harmans, J. Mooij, Science 299, 1869 (2003)
F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G.P. Lancaster, T. Deuschle, C. Becher, C.F. Roos, J. Eschner, R. Blatt, Nature 422, 408 (2003)
L.M. Vandersypen, M. Steffen, G. Breyta, C.S. Yannoni, M.H. Sherwood, I.L. Chuang, Nature 414, 883 (2001)
S. Bose, Phys. Rev. Lett. 91, 207901 (2003)
S. Bose, Contemp. Phys. 48, 13 (2007)
M. Takahashi, Thermodynamics of One-Dimensional Solvable Models (Cambridge University Press, 2005)
A. Bayat, S. Bose, Phys. Rev. A 81, 012304 (2010)
A. Bayat, L. Banchi, S. Bose, P. Verrucchi, Phys. Rev. A 83, 062328 (2011)
M. Christandl, N. Datta, A. Ekert, A. Landahl, Phys. Rev. Lett. 92, 187902 (2004)
A. Kay, Int. J. Quantum Inform. 08, 641 (2010) DOI:10.1142/S0219749910006514
C. Di Franco, M. Paternostro, M. Kim, Phys. Rev. Lett. 101, 230502 (2008)
R. Heule, C. Bruder, D. Burgarth, V.M. Stojanović, Phys. Rev. A 82, 052333 (2010)
H. Haselgrove, Phys. Rev. A 72, 062326 (2005)
A. Wójcik, T. Luczak, P. Kurzyński, A. Grudka, T. Gdala, M. Bednarska, Phys. Rev. A 72, 034303 (2005)
A. Wójcik, T. Luczak, P. Kurzyński, A. Grudka, T. Gdala, M. Bednarska, Phys. Rev. A 75, 022330 (2007)
N.Y. Yao, L. Jiang, A.V. Gorshkov, Z.X. Gong, A. Zhai, L.M. Duan, M.D. Lukin, arXiv:1011.2762 (2010)
S. Lorenzo, T. Apollaro, A. Sindona, F. Plastina, Phys. Rev. A 87, 042313 (2013)
S. Paganelli, S. Lorenzo, T.J. Apollaro, F. Plastina, G.L. Giorgi, Phys. Rev. A 87, 062309 (2013)
L. Banchi, T.J.G. Apollaro, A. Cuccoli, R. Vaia, P. Verrucchi, Phys. Rev. A 82, 052321 (2010)
L. Banchi, T. Apollaro, A. Cuccoli, R. Vaia, P. Verrucchi, New J. Phys. 13, 123006 (2011)
L. Banchi, T. Apollaro, A. Cuccoli, R. Vaia, P. Verrucchi, Nanomater. Nanotechnol. 1, 24 (2011)
T. Apollaro, L. Banchi, A. Cuccoli, R. Vaia, P. Verrucchi, Phys. Rev. A 85, 052319 (2012)
T.J. Apollaro, S. Lorenzo, F. Plastina, Int. J. Mod. Phys. B 27, 1345035 (2013)
M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000)
A. Fujiwara, P. Algoet, Phys. Rev. A 59, 3290 (1999)
R. Horodecki, M. Horodecki, Phys. Rev. A 54, 1838 (1996)
G. Bowen, S. Bose, Phys. Rev. Lett. 87, 267901 (2001)
M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. A 60, 1888 (1999)
D. Kretschmann, R.F. Werner, New J. Phys. 6, 26 (2004)
A. Koetsier, R.A. Duine, I. Bloch, H.T.C. Stoof, Phys. Rev. A 77, 023623 (2008)
P. Barmettler, A.M. Rey, E. Demler, M.D. Lukin, I. Bloch, V. Gritsev, Phys. Rev. A 78, 012330 (2008)
E. Lieb, T. Schultz, D. Mattis, Ann. Phys. 16, 407 (1961)
M. Christandl, N. Datta, T.C. Dorlas, A. Ekert, A. Kay, A.J. Landahl, Phys. Rev. A 71, 032312 (2005)
C. Albanese, M. Christandl, N. Datta, A. Ekert, Phys. Rev. Lett. 93, 230502 (2004)
M. Yung, S. Bose, Phys. Rev. A 71, 032310 (2005)
L. Banchi, A. Bayat, P. Verrucchi, S. Bose, Phys. Rev. Lett. 106, 140501 (2011)
A. Cantoni, P. Butler, Linear Algebra Appl. 13, 275 (1976)
B.N. Parlett, The Symmetric Eigenvalue Problem (SIAM, Philadelphia, 1998)
M. Bruderer, K. Franke, S. Ragg, W. Belzig, D. Obreschkow, Phys. Rev. A 85, 022312 (2012)
C. Albanese, M. Christandl, N. Datta, A. Ekert, Phys. Rev. Lett. 93, 230502 (2004)
L. Banchi, R. Vaia, J. Math. Phys. 54, 043501 (2013)
T.J. Osborne, N. Linden, Phys. Rev. A 69, 052315 (2004)
H.L. Haselgrove, Phys. Rev. A 72, 062326 (2005)
L. Campos Venuti, C. Degli Esposti Boschi, M. Roncaglia, Phys. Rev. Lett. 99, 060401 (2007)
C. Di Franco, M. Paternostro, D. Tsomokos, S. Huelga, Phys. Rev. A 77, 062337 (2008)
M. Markiewicz, M. Wieśniak, Phys. Rev. A 79, 054304 (2009)
N.Y. Yao, Z.X. Gong, C.R. Laumann, S.D. Bennett, L.M. Duan, M.D. Lukin, L. Jiang, A.V. Gorshkov, Phys. Rev. A 87, 022306 (2013)
P. Cappellaro, L. Viola, C. Ramanathan, Phys. Rev. A 83, 032304 (2011)
A. Ajoy, P. Cappellaro, Phys. Rev. A 85, 042305 (2012)
P. Badziag, M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. A 62, 012311 (2000)
A. Zwick, G. Álvarez, J. Stolze, O. Osenda, Phys. Rev. A 85, 012318 (2012) DOI:10.1103/PhysRevA.85.012318
A. Zwick, G.A. Álvarez, J. Stolze, O. Osenda, arXiv:1306.1695 (2013)
N.Y. Yao, L. Jiang, A.V. Gorshkov, P.C. Maurer, G. Giedke, J.I. Cirac, M.D. Lukin, Nature Commun. 3, 800 (2012)
Y. Ping, B.W. Lovett, S.C. Benjamin, E.M. Gauger, Phys. Rev. Lett. 110, 100503 (2013)
W. Bakr, J. Gillen, A. Peng, S. Fölling, M. Greiner, Nature 462, 74 (2009)
G.K. Brennen, C.M. Caves, P.S. Jessen, I.H. Deutsch, Phys. Rev. Lett. 82, 1060 (1999)
O. Mandel, M. Greiner, A. Widera, T. Rom, T. Hänsch, I. Bloch, Nature 425, 937 (2003) DOI:10.1038/nature02008
M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002)
J. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, S. Kuhr, Nature 467, 68 (2010)
W. Bakr, A. Peng, M. Tai, R. Ma, J. Simon, J. Gillen, S. Foelling, L. Pollet, M. Greiner, Science 329, 547 (2010)
M. Karski, L. Förster, J. Choi, A. Steffen, N. Belmechri, W. Alt, D. Meschede, A. Widera, New J. Phys. 12, 065027 (2010)
P. Cappellaro, C. Ramanathan, D. Cory, Phys. Rev. Lett. 99, 250506 (2007)
C. Ramanathan, P. Cappellaro, L. Viola, D. Cory, New J. Phys. 13, 103015 (2011)
A. Ajoy, R.K. Rao, A. Kumar, P. Rungta, Phys. Rev. A 85, 030303 (2012)
K.R.K. Rao, A. Kumar, Int. J. Quantum Inform. 10, 1250039 (2012)
F. Plastina, T.J.G. Apollaro, Phys. Rev. Lett. 99, 177210 (2007)
G. Gualdi, V. Kostak, I. Marzoli, P. Tombesi, Phys. Rev. A 78, 022325 (2008)
S.I. Doronin, A.I. Zenchuk, Phys. Rev. A 81, 022321 (2010)
J. Blaizot, G. Ripka, Quantum Theory of Finite Systems (MIT Press, 1986) ISBN 9780262022149
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Banchi, L. Ballistic quantum state transfer in spin chains: General theory for quasi-free models and arbitrary initial states. Eur. Phys. J. Plus 128, 137 (2013). https://doi.org/10.1140/epjp/i2013-13137-6
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DOI: https://doi.org/10.1140/epjp/i2013-13137-6