Would quantum computing be able to deanonymize CoinJoin transactions? Using the worst case scenario of this question, namely:


  Bitcoin ECDSA algorithm would be broken. Because quantum computers can easily decrypt the private key using the public key, anyone with a quantum computer can extract Bitcoins using the corresponding public key.


Given that quantum computers would be able to obtain private keys, would they be able to deanonymize CoinJoin transactions that are already present in the blockchain?
No.

CoinJoin does not rely on any cryptography to hide transaction flows. It merely combines multiple transactions into one, and randomizes the order of inputs and outputs.

Of course, as you point out, quantum computing would allow stealing ECDSA outputs...