Quantum entanglement in states generated by bilocal group algebras

Details Quantum entanglement in states generated by bilocal group algebras Quantum entanglement in states generated by bilocal group algebras

2005-04-07

arxiv.org/abs/quant-ph/0504049v2

Phys.Rev. A 72, 012324 (2005)

Physics

Quantum Physics

9 pages, no figs; updated to the published version

Scientific paper

10.1103/PhysRevA.72.012324

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 2-colorable (i.e., bipartite) graph states and they include GHZ, cluster states etc. Examples include an application to qudits and a calculation of the n-tangle for 2-colorable graph states.

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