In this paper, two quantum key agreement protocols are proposed, which can resist against the collective-dephasing noise and the collective-rotation noise, respectively. These two protocols mainly utilize logical quantum states, the measurement correlation property of multi-particle entangled states and the delayed measurement technique. Moreover, they have no information leakage and are congenitally free from the Trojan horse attacks. The use of the decoy state technology and the delayed measurement technique makes them secure against both participant and outsider attacks. The efficiency analysis shows that the two protocols are very efficient.