Quantum entanglement in states generated by bilocal group algebras

Alioscia Hamma, Radu Ionicioiu, and Paolo Zanardi
Phys. Rev. A 72, 012324 – Published 20 July 2005

Abstract

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 Greenberger-Horne-Zeilinger, cluster states, etc. Examples include an application to qudits and a calculation of the n-tangle for 2-colorable graph states.

  • Received 7 April 2005

DOI:https://doi.org/10.1103/PhysRevA.72.012324

©2005 American Physical Society

Authors & Affiliations

Alioscia Hamma, Radu Ionicioiu, and Paolo Zanardi

  • Quantum Information Group, Institute for Scientific Interchange (ISI), Viale Settimio Severo 65, I-10133 Torino, Italy

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Issue

Vol. 72, Iss. 1 — July 2005

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