Yoshida Masakazu, Nakayama Ayumu, Cheng Jun
Faculty of Design Technology, Osaka Sangyo University, 3-1-1 Daito-shi, Osaka 574-8530, Japan.
Independent Researcher, Chiba 263-8522, Japan.
Entropy (Basel). 2020 Nov 11;22(11):1275. doi: 10.3390/e22111275.
We introduce a quantum key distribution protocol using mean multi-kings' problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users' information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users' systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper's extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability.
我们介绍一种使用平均多王问题的量子密钥分发协议。通过该协议，发送方能够与接收方共享一个比特序列作为秘密密钥。我们考虑窃听者获得的信息增益与合法用户信息中所含干扰之间的关系。在BB84协议中，这种关系被称为所谓的信息干扰定理。我们关注的场景是，发送方和两个接收方试图共享比特序列，而窃听者试图通过与合法用户的系统以及一个辅助系统相互作用来提取信息。我们推导出了与窃听者对应的比特序列的量子态可区分性和与合法用户共享的比特序列的错误概率之间的权衡不等式。我们的不等式表明，窃听者提取关于秘密密钥的信息不可避免地会导致状态受到干扰并增加错误概率。
