Secure Quantum Key Distribution Based on a Special Deutsch-Jozsa Algorithm

Koji Nagata, Tadao Nakamura, Han Geurdes, Josep Batle, Soliman Abdalla, Ahmed Farouk

Abstract


Recently, secure quantum key distribution based on Deutsch's algorithm using the Bell state is reported [1]. Our aim is of extending the result to a multipartite system. In this paper, we propose a highly speedy key distribution protocol. We present secure quantum key distribution based on a special Deutsch-Jozsa algorithm using Greenberger-Horne-Zeilinger states. Originally, Bob has promised to use a function $f$ which is of one of the two kinds; either the value of $f(x)$ is constant for all $x$, or the value of $f(x)$ is balanced, that is, it is equal to $1$ for exactly half of all the possible $x$, and $0$ for the other half. Here, Bob uses a special function when it is not constant. We may say the value of $f(x)$ is special. Our quantum key distribution overcomes a classical counterpart by a factor $O(2^N)$.

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