So the first company that can break bitcoin addresses using quantum computers gets a prize of how many billion(?) dollars by stealing all the non-migrated addresses.
A very interesting philosophical and moral can of worms you just opened there. Bitcoin is governed by the protocol, so if the protocol permits anyone who can sign a valid transaction involving a given UTXO to another address, then it technically isn't a "crime". Morally I'm not sure I'd be able to sleep well at night if I unilaterally took what I didn't exchange value for.
As for the forgotten key case, I think the only way to prove you had the key at some point would need to involve the sender vouching for you and cryptographically proving they were the sender.
A very interesting philosophical and moral can of worms you just opened there. Bitcoin is governed by the protocol, so if the protocol permits anyone who can sign a valid transaction involving a given UTXO to another address, then it technically isn't a "crime". Morally I'm not sure I'd be able to sleep well at night if I unilaterally took what I didn't exchange value for.
As for the forgotten key case, I think the only way to prove you had the key at some point would need to involve the sender vouching for you and cryptographically proving they were the sender.