Abstract
In the quest for the achievement of realistic quantum state transfer protocols, relaxing the required conditions is a fundamental step. The use of multi-particle systems for the purpose of quantum information processing is made hard by a number of technical difficulties, related in particular to the lack of addressability of their single elements. We have thus to research novel ways to bypass these problems. Even if investigating the whole evolution of a quantum system is surely interesting, considering the behaviour of a few characteristic features could help us to find striking strategies in the context outlined above. This is exactly the idea at the basis of the method presented in this chapter, which we name information flux approach. Through it, we can design protocols for quantum state transfer in limited-control scenarios. In particular, we focus our interest in finding a way to avoid the initialisation of the spin chain. Different cases are described throughout the chapter.
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- 1.
Throughout this chapter, the XX model has been taken as \(\sum _{i=1}^{N-1}J_{i}(\hat{X}_{i}\hat{X}_{i+1} +\hat{ Y }_{i}\hat{Y }_{i+1})\). For this reason, when the parameters follow the pattern \(J_{i} = J\sqrt{i(N - i)}\), the time corresponding to perfect state transfer is \(t =\pi /(4J)\).
References
C. Di Franco, M. Paternostro, G. M. Palma, M. S. Kim, Phys. Rev. A 76, 042316 (2007); C. Di Franco, M. Paternostro, G. M. Palma, Int. J. Quant. Inf. 6(Supp. 1), 659 (2008)
S. Bose, Contemp. Phys. 48, 13 (2007)
M. Christandl, N. Datta, A. Ekert, A. J. Landahl, Phys. Rev. Lett. 92, 187902 (2004); C. Albanese, M. Christandl, N. Datta, A. Ekert, Phys. Rev. Lett. 93, 230502 (2004); G. M. Nikolopoulos, D. Petrosyan, P. Lambropoulos, Europhys. Lett. 65, 297 (2004); G. M. Nikolopoulos, D. Petrosyan, P. Lambropoulos, J. Phys.: Condens. Matter 16, 4991 (2004); M. Christandl, N. Datta, T. C. Dorlas, A. Ekert, A. Kay, A. J. Landahl, Phys. Rev. A 71, 032312 (2005)
S. Bose, Phys. Rev. Lett. 91, 207901 (2003)
S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999); E. Lieb, T. Schultz, D. Mattis, Ann. Phys. 16, 407 (1961)
C. Di Franco, M. Paternostro, D. I. Tsomokos, S. F. Huelga, Phys. Rev. A 77, 062337 (2008)
Y. Makhlin, G. Schön, A. Schnirman, Rev. Mod. Phys. 73, 357 (2001); D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, C. Urbina, D. Esteve, M. H. Devoret, Science 296, 886 (2002); D. I. Tsomokos, M. J. Hartmann, S. F. Huelga, M. B. Plenio, New J. Phys. 9, 79 (2007)
C. Di Franco, M. Paternostro, M. S. Kim, Phys. Rev. A 81, 022319 (2010)
A. O. Lyakhov, C. Bruder, Phys. Rev. B 74, 235303 (2006)
A. Wojcik, T. Luczak, P. Kurzynski, A. Grudka, T. Gdala, M. Bednarska, Phys. Rev. A 72, 034303 (2005)
D. P. DiVincenzo, in Mesoscopic Electron Transport, eds. by L. Kowenhoven, G. Schön, L. Sohn (Kluwer, Dordrecht, 1997).
N. Gershenfeld, I. L. Chuang, Science 275, 350 (1997)
S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, R. Schack, Phys. Rev. Lett. 83, 1054 (1999)
G. De Chiara, D. Rossini, S. Montangero, R. Fazio, Phys. Rev. A 72, 012323 (2005); D. Burgarth, Eur. Phys. J. Special Topics 151, 147 (2007); M. Wiesniak, arXiv:0711.2357; L. Zhou, J. Lu, T. Shi, C. P. Sun, arXiv:quant-ph/0608135
J. Fitzsimons, J. Twamley, Phys. Rev. Lett. 97, 090502 (2006)
C. Di Franco, M. Paternostro, M. S. Kim, Phys. Rev. Lett. 101, 230502 (2008); C. Di Franco, M. Paternostro, M. S. Kim, LNCS 6519, 168 (2011)
C. Di Franco, M. Paternostro, M. S. Kim, Phys. Rev. A 77, 020303(R) (2008)
D. M. Greenberger, M. A. Horne, A. Zeilinger, in Bell Theorem, Quantum Theory, and Conceptions of the Universe, ed. by M. Kafatos (Kluwer, Dordrecht, 1989)
E. Knill, R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)
S. Parker, M. B. Plenio, Phys. Rev. Lett. 85, 3049 (2000)
R. Raussendorf, H.-J. Briegel, Phys. Rev. Lett. 86, 5188 (2001)
M. Hein, J. Eisert, H.-J. Briegel, Phys. Rev. A 69, 062311 (2004); H.-J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, M. Van den Nest, Nat. Phys. 5, 19 (2009)
M.-H. Yung, S. Bose, Phys. Rev. A 71, 032310 (2005); P. Karbach, J. Stolze, Phys. Rev. A 72, 030301(R) (2005)
T. J. G. Apollaro, A. Cuccoli, C. Di Franco, M. Paternostro, F. Plastina, P. Verrucchi, New J. Phys. 8, 083046 (2010)
M. Markiewicz, M. Wiesniak, Phys. Rev. A 79, 054304 (2009); see also A. Kay, Int. J. Quant. Inf. 8, 641 (2010)
Acknowledgements
CDF and MP’s work was supported by the UK EPSRC with a grant under the “New Directions for EPSRC Research Leaders” initiative (EP/G004759/1). MSK’s work was supported by the grant NPRP 4-554-1-094 from Qatar National Research Fund. MP thanks the UK EPSRC for a Career Acceleration Fellowship.
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Franco, C.D., Paternostro, M., Kim, M.S. (2014). Quantum State Transfer with Limited Resources. In: Nikolopoulos, G., Jex, I. (eds) Quantum State Transfer and Network Engineering. Quantum Science and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39937-4_4
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