
Given a finite group G with a bilocal representation,
we investigate the bipartite entanglement in the state constructed from
the group algebra of G acting on a separable reference state. We find
an upper bound for the von Neumann entropy for a bipartition (A,B) of
a quantum system and conditions to saturate it.
We show that these states can be interpreted as ground states of generic
Hamiltonians or as the physical states in a quantum gauge theory and that
under specific conditions their geometric entropy satisfies the entropic
area law.
If G is a group of spin flips acting on a set of qubits, these states
are locally equivalent to 2colorable (i.e., bipartite) graph states and
they include GHZ, cluster states etc. Examples include an application
to qudits and a calculation of the ntangle for 2colorable graph states.
