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I don't think moving old coins could very well be hidden. But, I believe the reason people say that old coins are more likely targets is because a person with a quantum computer doesn't have to race to crack the key. If they target a transaction in mempools, they have to crack the key before the transaction gets mined.
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I suppose if I was part a group of rogue developers that had access to quantum computers capable of cracking ECDLP based signatures I would go after bitcoins that have supposedly been lost to time or otherwise considered unrecoverable and then use a post quantum-based script to be able to disguise the transaction. I dont know about warning, but time certainly.
That is of course assuming that quantum technology has the capabilities of hacking into someones bitcoins stash, or would these computers only have the capability to attack live transactions currently being broadcasted through the blockchain?