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On the security of the quantum key distribution using the Mean King Problem

It is anticipated that quantum key distribution enable us to share a secret key while guaranteeing unconditionally security. In this paper, we discuss the quantum key distribution using the Mean King Problem which was proposed by J. Bub in 2001. While this two-way quantum protocol is essentially different from the other one-way protocols like the BB84, it has been shown that Eve cannot gain any information without being detected even in this protocol. Assuming two attack scenarios in this protocol, we derive two trade-off inequalities showing that the larger Eve's information gain is, the higher the detectability becomes. These quantitative inequalities enables the legitimate users to estimate Eve's information gain.