2. Notification transactions still exist but no longer leave a privacy footprint on the blockchain. Instead, a notification transaction is simply a single OP_RETURN containing a value that only Alice and Bob can calculate. If Alice's notification transaction uses UTXOs not associated with her identity, there is never a footprint showing that either her or Bob are using private payments. If Alice uses tainted coins, only she is exposed as a user of Private Payments but Bob still isn't.
That's a neat trick. What about not using OP_RETURN at all, and just publishing on a tor hidden service that other wallets check? Alice wouldn't have to expose on-chain that she is a sender of a private payment.
- Bryan