N -level ghost spins and entanglement

Ghost spins, 2-level spinlike variables with indefinite norm have been studied in previous work. Here we explore various N-level generalizations of ghost spins. First we discuss a flavored generalization comprising N copies of the ghost-spin system, as well as certain ghost-spin chains which in the continuum limit lead to 2-dim bc-ghost conformal field theorys with O(N) flavor symmetry. Then we explore a symplectic generalization that involves antisymmetric inner products, and finally a ghost-spin system exhibiting N irreducible levels. We also study entanglement properties. In all these cases, we show the existence of positive norm "correlated ghost spin" states in two copies of ghost-spin ensembles obtained by entangling identical ghost spins from each copy: these exhibit positive entanglement entropy.