Abstract
In this paper, we consider the modified generalization of the Deutsch-Jozsa algorithm in the d-level (qudits) quantum system to determine the types of the function f (constant or linear) that had been used. A comparison of the efficiency between the quantum algorithm and the classical case have been given. In addition, the quantum key distribution protocol based on the algorithm is established to show the contribution of our work to the improvement in the detecting the Eve’s attack that occurs in the protocol based on the original Deutsch-Jozsa algorithm.
Similar content being viewed by others
References
Von Neumann, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton. In: New Jersey ((1955))
Feynman, R.P., Leighton, R.B., Sands, M.: Lectures on Physics. Volume III. Quantum mechanics. In: Addison-Wesley Publishing Company ((1965))
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, UK (2000)
Feynman, R.P.: Simulating Physics with Computers. Int. J. Theor. Phys. 21, 6 (1982)
Yanofsky, N.S., Mannucci, M.A.: Quantum Computing for Computer Scientists. Cambridge University Press, Cambridge, UK (2008)
Shor, P.W.: Algorithms for quantum computation discrete logarithms and factoring. IEEE Computer Society Press. 124–134 ((1994))
Grover, L.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325 (1997)
Deutsch, D., Jozsa, R.: Rapid solutions of problems by quantum computation. Proceedings of the Royal Society of London A. (1992)
Cleve, R., Ekert, A., Macchiavello, C., Mosca, M.: Quantum algorithms revisited. Proceedings of the Royal Society of London A. 454, 339–354 (1998)
Chi, D.P., Kim, J., Lee, S.: Initialization-free generalized Deutsch–Jozsa algorithm. J. Phys. A: Math. Gene. 34, 5251–5258 (2001)
Nagata, K., Nakamura, T., Geurdes, H., Batle, J., Abdalla, S., Farouk, A., Diep, D.N.: Creating Very True Quantum Algorithms for Quantum Energy Based Computing. Int. J. Theor. Phys. 57, 973–980 (2018)
Nagata, K., Nakamura, T.: Can von Neumann’s Theory Meet the Deutsch-Jozsa Algorithm? Int. J. Theor. Phys. 49, 162–170 (2010)
Nagata, K., Nakamura, T.: The Deutsch-Jozsa Algorithm Can Be Used for Quantum Key Distribution. Open Access Library Journal. 2, e1798 (2015)
Nagata, K., Nakamura, T. and Farouk, A.:Quantum Cryptography Based on the Deutsch-Jozsa Algorithm. Int. J. Theor. Phys. 56, 2887-2897 (2017)
Nagata, K., Nakamura, T., Geurdes, H., Batle, J., Abdalla, S., Farouk, A.: Secure Quantum Key Distribution Based on a Special Deutsch-Jozsa Algorithm. Asian J. Math. Phys. 2, 6–13 (2018)
Daniel, G.: Fault-tolerant quantum computation with higher-dimensional systems. In: Quantum Computing and Quantum Communications, pp. 302–313, Springer Berlin Heidelberg (1999)
Muthukrishnan, A., Stroud, C.R.: Multivalued logic gates for quantum computation. Phys. Rev. A. 62 ((2000))
Acknowledgments
This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF-2016R1D1A1B03934653).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nguyen, D.M., Kim, S. Quantum Key Distribution Protocol Based on Modified Generalization of Deutsch-Jozsa Algorithm in d-level Quantum System. Int J Theor Phys 58, 71–82 (2019). https://doi.org/10.1007/s10773-018-3910-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-018-3910-4