Abstract
We propose a probabilistic quantum protocol to realize a nonlinear transformation of qutrit states, which by iterative applications on ensembles can be used to distinguish two types of pure states. The protocol involves single-qutrit and two-qutrit unitary operations as well as post-selection according to the results obtained in intermediate measurements. We utilize the nonlinear transformation in an algorithm to identify a quantum state provided it belongs to an arbitrary known finite set. The algorithm is based on dividing the known set of states into two appropriately designed subsets, which can be distinguished by the nonlinear protocol. In most cases, this is accompanied by the application of some properly defined physical (unitary) operation on the unknown state. Then, applying the nonlinear protocol, one can decide which of the two subsets the unknown state belongs to, thus reducing the number of possible candidates. By iteratively continuing this procedure until a single possible candidate remains, one can identify the unknown state.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. T. Pegg, L. S. Phillips, and S. M. Barnett, Phys. Rev. Lett., 81, 1604 (1998).
M. Koniorczyk, Z. Kurucz, A. Gábris, and J. Janszky, Phys. Rev. A, 62, 013802 (2000).
H. Nakazato, T. Takazawa, and K. Yuasa, Phys. Rev. Lett., 90, 060401 (2003).
H. Aschauer, W. Dür, and H.-J. Briegel, Phys. Rev. A, 71, 012319 (2005).
J. Combes and K. Jacobs, Phys. Rev. Lett., 96, 010504 (2006).
P. J. Coles and M. Piani, Phys. Rev. A, 89, 010302 (2014).
A. Streltsov, H. Kampermann, and D. Brus, Phys. Rev. Lett., 106, 160401 (2011).
L.-A. Wu, D. A. Lidar, and S. Schneider, Phys. Rev. A, 70, 032322 (2004).
P. V. Pyshkin, E. Y. Sherman, D.-W. Luo, and J. Q. You, Phys. Rev. B, 94, 134313 (2016).
I. A. Luchnikov and S. N. Filippov, Phys. Rev. A, 95, 022113 (2017).
Y. Li, L.-A. Wu, Y.-D. Wang, and L.-P. Yang, Phys. Rev. B, 84, 094502 (2011).
P. V. Pyshkin, D.-W. Luo, J. Q. You, and L.-A. Wu, Phys. Rev. A, 93, 032120 (2016) (b).
J. B. Hertzberg, T. Rocheleau, T. Ndukum, and C. Macklin, Nature Phys., 6, 213 (2010).
T. Rocheleau, T. Ndukum, C. Macklin, and J. B. Hertzberg, Nature, 463, 72 (2010).
A. Gilyén, T. Kiss, and I. Jex, Sci. Rep., 6, 20076 (2015).
M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2000).
S. M. Barnett and S. Croke, Adv. Opt. Photon., 1, 238 (2009).
J. Bae and L.-C. Kwek, J. Phys. A: Math. Theor., 48, 083001 (2015).
H. Mack, D. G. Fischer, and M. Freyberger, Phys. Rev. A, 62, 042301 (2000).
J. M. Torres, J. Z. Bernád, G. Alber, et al., Phys. Rev. A, 95, 023828 (2017).
W.-H. Zhang and G. Ren, Quantum Inform. Process., 17, 155 (2018).
O. Kálmán and T. Kiss, Phys. Rev. A, 97, 032125 (2018).
J.-S. Xu, M.-H. Yung, X.-Y. Xu, et al., Nature Photon., 8, 113 (2014).
A. Abdumalikov Jr, M. Fink, K. Juliusson, et al., Nature, 496, 482 (2013).
A. Hayashi, M. Horibe, and T. Hashimoto, Phys. Rev. A, 72, 052306 (2005).
A. Hayashi, M. Horibe, and T. Hashimoto, Phys. Rev. A, 73, 012328 (2006).
U. Herzog and J. A. Bergou, Phys. Rev. A, 78, 032320 (2008).
U. Herzog, Phys. Rev. A, 94, 062320 (2016).
A. Hayashi, T. Hashimoto, and M. Horibe, Phys. Rev. A, 78, 012333 (2008).
A. M. Chudnov, Discrete Math. Appl., 25, 69 (2015).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pyshkin, P.V., Gábris, A., Kálmán, O. et al. Quantum State Identification of Qutrits via a Nonlinear Protocol. J Russ Laser Res 39, 456–464 (2018). https://doi.org/10.1007/s10946-018-9740-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-018-9740-2