**Entangled subspaces and generic local state discrimination with pre-shared entanglement** - Benjamin Lovitz

It is of fundamental importance to determine the most useful entangled quantum states for non-local quantum information processing tasks. While this problem is quite well-understood in the bipartite (two-party) setting, comparatively little is known in the multipartite (more-than-two-party) setting. In this talk, we endeavour to determine the most useful entangled states for the particular task of local unambiguous state discrimination. We measure "how useful" a particular entangled state |phi> is for this task by the maximum number of generic pure states that local parties can unambiguously discriminate when they can use |phi> as a resource state to implement their local measurement. We determine that this number is equal to the Krull dimension of the Zariski closure of the set of pure states obtainable from |phi> by SLOCC. This dimension is known for several resource states, for example the GHZ state. Somewhat surprisingly, *almost all* resource states |phi> maximize this dimension, and hence are maximally useful for local state discrimination. Time permitting, we will also present related results on entangled subspaces, which are linear subspaces of multipartite space for which every element is "entangled" in some way. This talk is based on joint work with Nathaniel Johnston (arXiv:2010.02876).