The framing of this question is just completely wrong, and I'd go so far as to suggest the question doesn't belong on Security SE but Worldbuilding SE if you're trying to make up a world where it does make sense. You don't carry sensitive information in cleartext, and you don't destroy media to make information inaccessible. You make proper use of encryption, and you either don't carry the key at all, or destroy the key in emergency rather than destroying the media the (potentially large) data is stored on.
The updates to the question about encryption are just wrong as well. "Torture to get the key" is not an issue because the key is not something small enough to be something you know. Either you don't possess it at all, or you possess it in a form that's easily destroyed (e.g. soluble or ingestable paper). There are plenty of forms of encryption which are not even theoretically susceptible to QC, and even for ones that are, most of the susceptibility is "theoretical" in that it relies on abstract mathematical objects that almost surely can never exist in reality. (But if you don't believe me on this last point, just choose something post-quantum.)