  We study patterns of quantum entanglement in systems of spins and ghost-spins
regarding them as simple quantum mechanical toy models for theories containing
negative norm states. We define a single ghost-spin as in arXiv:1602.06505
[hep-th] as a 2-state spin variable with an indefinite inner product in the
state space. We find that whenever the spin sector is disentangled from the
ghost-spin sector (both of which could be entangled within themselves), the
reduced density matrix obtained by tracing over all the ghost-spins gives rise
to positive entanglement entropy for positive norm states, while negative norm
states have an entanglement entropy with a negative real part and a constant
imaginary part. However when the spins are entangled with the ghost-spins,
there are new entanglement patterns in general. For systems where the number of
ghost-spins is even, it is possible to find subsectors of the Hilbert space
where positive norm states always lead to positive entanglement entropy after
tracing over the ghost-spins. With an odd number of ghost-spins however, we
find that there always exist positive norm states with negative real part for
entanglement entropy after tracing over the ghost-spins.
