Quantum Cryptography Based on the Deutsch-Jozsa Algorithm

Abstract

Recently, secure quantum key distribution based on Deutsch's algorithm using the Bell state is reported (Nagata and Nakamura, Int. J. Theor. Phys. doi:10.1007/s10773-017-3352-4, 2017). Our aim is of extending the result to a multipartite system. In this paper, we propose a highly speedy key distribution protocol. We present sequre quantum key distribution based on a special Deutsch-Jozsa algorithm using Greenberger-Horne-Zeilinger states. Bob has promised to use a function f which is of one of two kinds; either the value of f(x) is constant for all values of x, or else the value of f(x) is balanced, that is, equal to 1 for exactly half of the possible x, and 0 for the other half. Here, we introduce an additional condition to the function when it is balanced. Our quantum key distribution overcomes a classical counterpart by a factor O(2 (N) ).