I thought that unitarity was also preserved in quantum mechanics, which is linked to the law of preservation of information , which induces reversibility. This was the central question about black holes destroying information being a problem, which gives rise to the problem of black hole firewalls. If information is truly destroyed, then quantum mechanics has a deep flaw
Even if information can be destroyed ("erased"), it is not by way of reversing the process that lead to its creation, the latter thus being necessarily non-unitary. This, in fact, is a requisite for the notion of measurement to make any sense.
The point here is to consider what the claimed "non-reversible process" means in a quantum theory that as of current does _not_ allow for destruction of information.