Quantum conference key agreement with phase noise resistance

The Quantum Conference Key Agreement (QCKA) protocol, also known as multi-party key distribution, aims fundamentally to enable two or more participants to establish a shared key through quantum channels. During the negotiation and communication processes, noise inevitably affects the system, causing particles in maximally entangled states to transition into non-maximally entangled states. In this article, we propose a QCKA protocol based on non-maximally entangled Greenberger–Horne–Zeilinger (GHZ) states. These GHZ states can have different parameters without requiring specific values, thereby reducing our reliance on channel conditions. On the other hand, considering the influence of environmental noise, we employ the logical GHZ states to counteract the collective phase noise. Compared to previous protocols, our method simplifies the negotiation process and extends the applicability of the GHZ channel. During the protocol, we can perform key agreement without explicitly specifying the parameters of the quantum states, enhancing convenience. Furthermore, security analysis demonstrates that our protocol can effectively prevent attacks from both participants and external entities, including interception-resend attacks, measurement-resend attacks, Trojan horse attacks, and entanglement measurement attacks.