The issue of free-riding often exists in regional air pollution collaborative governance. To effectively address this issue, a quantum game model involving two heterogeneous governments was constructed using quantum game theory. The consideration of entangled states was discussed separately, and the game results were locked into a quantum version of cooperation strategies through strategy expansion. Based on the interpretation of quantum strategies and quantum entanglement, explicit provisions for the "entanglement agreement" in intergovernmental collaboration were made. The results show that entangled states and quantum strategies can effectively address the free-riding issue of governments. Quantum entanglement and quantum strategies, through interest association and index quantification, can avoid the issue of "moral hazard" and strengthen the binding force on both governments to fulfill their responsibilities. Based on the conclusions, three policy implications were proposed: promoting the digital transformation of local governments and establishing an air quality information-sharing platform, improving the performance evaluation and accountability mechanism for collaborative air pollution governance, fostering regional identity and establishing intergovernmental trust. These implications provide decision-making references for advancing regional air pollution collaborative governance in China.