Abstract
Given a finite group with a bilocal representation, we investigate the bipartite entanglement in the state constructed from the group algebra of acting on a separable reference state. We find an upper bound for the von Neumann entropy for a bipartition 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 is a group of spin flips acting on a set of qubits, these states are locally equivalent to 2-colorable (i.e., bipartite) graph states and they include Greenberger-Horne-Zeilinger, cluster states, etc. Examples include an application to qudits and a calculation of the -tangle for 2-colorable graph states.
- Received 7 April 2005
DOI:https://doi.org/10.1103/PhysRevA.72.012324
©2005 American Physical Society