Cessation of Existence is incompatible with the leading models of "standard physics" as presented at the level of core grad school physics classes. Now, I don't entirely subscribe to those models but I do understand them well enough to have aced all my core theory classes (lab was a shameful B...) so I actually have 'more weight' to my claim here than it might appear. "Conservation of information" is absolutely a thing in "the Standard Model", it is just that the information becomes non-localized and (in the Everett interpretation) spread across timelines. But the information that was "you" (using the model that seems standard on LW that 'you' are a collection of organized data) should, in theory, persist indefinitely into the future.

Quantum information is a very different thing from what you're thinking of as "information" (ie: data stored on a hard-disk or connection strengths in a neural net). For one thing, turning quantum information into "normal" information actually requires becoming entangled (in causal contact) with the quantum information, which is an entropic process. Particularly, the disequilibriating entropic process composing your consciousness is, you know, entropic, so it requires fresh sources of unentangled information and mechanical energy in order to operate (luckily, stored chemical energy in food can provide both).

Sorry for being vague; I wish I had the mathematical knowledge to explain this more clearly.