Abstract: Quantum key agreement (QKA) protocols allow participants to negotiate a classical shared secret key fairly via public quantum channels. Furthermore, the shared key cannot be determined independently by any subset of the participants. Their security is assured by the quantum mechanics principles, so they can achieve unconditional security and have drawn considerable attention. Based on four-particle entangled states and logical qubits, two robust two-party quantum key agreement protocols against collective-dephasing noise and collective-rotation noise are proposed. The security analysis shows that the two protocols can not only resist against participant attacks and outsider attacks, but also resist against two kinds of Trojan horse attacks. Furthermore, the two protocols also achieve higher qubit efficiency.