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 Year 1600, your ship sinks with a chest full of gold 

Year 2000 someone builds a submarine and recovers it

Year 2012 you lose a hard drive with 1000 BTC on it

Year 2040 someone builds a quantum computer and recovers it 

Should the saying "finders keepers" apply? 
 There is no alternative so yes 
 Yes 
 "The new Bitcoin gold rush" 
 Holding the keys is 10 / 10ths of the law with Bitcoin. The test is: 
1) Can you move it around on chain? 
2) Did you get that ability without subverting another person’s same ability?
If yes to both, then enjoy it. 
 Finders keepers  
 absolutely yes 
 commies will hate this 
 Yes. FULL STOP 
 By the time it's feasible to do so, I think everyone actively using Bitcoin (I.e. hasn't lost their keys) will have moved any significant sum to some sort of novel quantum-difficult wallet.

Realistically, there may also be some sort of regulation (or at least convention) beyond simple finders-keepers by then.