Properties of Generic Subspaces - Jonathan Walgate

We show how a simple fact of algebraic geometry translates into quantum information theory, determining when subspaces of multipartite Hilbert space have certain generic properties. In particular, we show when subspaces are completely entangled. This in turn implies other results concerning the local distinguishability of random quantum states, the separability of random mixed states, the indistinguishability of random subspaces, and a mathematically interesting generalisation of Schmidt rank.