The glitch with Quantum Conundrum not appearing as "Purchased" in the Playstation Store appears to be due to the bundling of the game with Tomb Raider. If you have your download receipts saved, try to find the one for "Tomb Raider Bundle" to determine on what date you bought that bundle (it will be sometime after March 3, 2013). Then search through your download list for the games you bought on that date and the demo and unlock for Quantum Conundrum will probably be there.
If the above doesn't work, try to figure out when the last date was that you renewed your Playstation Plus subscription and check that date in your download list. Free Plus games usually change dates in your download list, moving up to your last renewal date.
It is very annoying, though, that the game appears to be unpurchased in the Store, making it easy to accidentally re-buy something you already own.
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