Indistinguishability under chosen plaintext attack (IND-CPA) is a crucial security notion for assessing the confidentiality of encryption algorithms. Unlike in the classical scenario, this notion is more diverse in the quantum realm, giving rise to several variants. Carstens et al. (TCC’21) have studied the relationships between various quantum IND-CPA notions, revealed the close correlation between the quantum security of cryptographic primitives and the query model employed. In this paper, we focus on the quantum IND-CPA security of authenticated encryption with associated data (AEAD). AEADs provide confidentiality and integrity for both the message and associated data (AD). However, we find that the presence of AD invalidates the quantum query models introduced in prior works. To address this issue, we introduce a new quantum query model tailored for AEAD. Based on this model, we provide a comprehensive analysis of the relationships, including implications and non-implications, between different quantum IND-CPA security notions when the target algorithm is an AEAD scheme. In addition, we explore the connection between the quantum implementation of encryption primitives and their post-quantum security.