Abstract: Quantum cryptography leverages unique features of quantum mechanics in order to construct cryptographic primitives which are oftentimes impossible for digital computers. Cryptographic applications of quantum computers therefore have the potential for useful quantum advantage – entirely without computational speed-ups. In this talk, I will focus on two fundamental questions: First, is it possible to certify that private data has been deleted? And second, is it possible to revoke a cryptographic key? I show how quantum computers can answer these questions affirmatively through the use of lattice-based cryptography; in particular, by making use of Gaussian superpositions over lattices.