In this paper, two two-party quantum key agreement protocols are proposed with logical chi-states and logical Bell states. These two protocols can be immune to the collective-dephasing noise and the collective-rotation noise, respectively. They make full use of the measurement correlation property of multi-particle entangled states and the delayed measurement technique. This ensures that two participants can exchange the secret keys of each other and fairly establishes a shared key. There is no information leakage problem when establishing a shared key. The use of the delayed measurement technique and the decoy state technology makes the two protocols resist against both participant and outsider attacks. Furthermore, the two protocols are congenitally free from the Trojan horse attacks and have high qubit efficiency.