Abstract: An encryption scheme is called indistinguishable under chosen plaintext attack (short IND-CPA), if an attacker cannot distinguish the encryptions of two messages of his choice. Alternatively there are other variants of this definition, that all turn out to be equivalent in the classical case. However in the quantum case, there is a lack of a comprehensive study of all quantum versions of IND-CPA security notion. We give an overview of these different variants of quantum IND-CPA for symmetric encryption schemes. In total, 57 different notions are valid and achievable. We investigate the relations between these notions and prove various equivalences, implications, non-equivalences, and non-implications between these variants. Some of non-implications are left as conjectures and need further research.