Homological invariants of stabilizer states

Abstract

We propose a new kind of invariant of multi-party stabilizer states with respect to local Clifford equivalence. These homological invariants are discrete entities defined in terms of the entanglement a state enjoys with respect to arbitrary groupings of the parties, and they may be thought of as reflecting entanglement in a qualitative way. We investigate basic properties of the invariants and link them with known results on the extraction of GHZ states.