According to the peculiar entanglement and measurement properties of the three-particle GHZ state, we have systematically analyzed that two GHZ states and three GHZ states satisfy some expressions after exchanging one or two groups of particles respectively, which are described as four interesting and flexible equations. The four equations can deduce that four GHZ states or even m GHZ states still satisfy some expressions after exchanging one group and two groups of particles, and they can be summarized as two general flexible equations. Furthermore, we also investigate their application in the field of quantum key agreement based on these equations. In particular, we combine with decoy photons to propose a novel session key sharing protocol, which can guarantee the unconditional security of the protocol. It is feasible to use the existing quantum processing technology to realize the proposed protocol.

根据三粒子GHZ态特有的纠缠和测量性质，我们系统地分析了两个GHZ态和三个GHZ态分别交换一组或两组粒子后满足一些表达式，描述为四个有趣且灵活的方程. 这四个方程可以推导出四个GHZ状态甚至mGHZ态在交换一组和两组粒子后仍然满足一些表达式，它们可以概括为两个通用的柔性方程。此外，我们还基于这些方程研究了它们在量子密钥协议领域的应用。特别是，我们结合诱饵光子提出了一种新颖的会话密钥共享协议，可以保证协议的无条件安全。使用现有的量子处理技术来实现所提出的协议是可行的。