The creation of a "Hive-Mail vault" requires both the Private Posting Key and the Private Memo Key. The Active Key isn't used anywhere, for security reasons.

Specifically, the Posting Key is used to sign "custom_json" and "account_update2" operations. The custom_json are used for sending encrypted messages onchain, and the account_update2 are used to update the user's Posting Metadata with the updated Public Post-Quantum Key.

The Memo Key is used as an additional security element, alongside the Post-Quantum Key, to encrypt messages.

No Hive keys are required to create or update your Post-Quantum key pairs, but you will need your Posting Key in order to update it onchain (with an account_update2 operation).

Now, to read messages directed to you, you need only your Private Memo Key and Private Post-Quantum Key. The Posting Key isn't used for that.