Quantum entanglement in states generated by bilocal group algebras

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

9 pages, no figs; updated to the published version

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• Topological order and topological entropy in classical systems
• Disk entanglement entropy for a Maxwell field
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• Mutual information area laws for thermal free fermions
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• A complete characterization of the spectrum of the Kitaev model on spin ladders
• Entanglement Properties of Gauge Theories from Higher-Form Symmetries
• Thermalization of Topological Entropy after a Quantum Quench
• Quantum Coherence in Ergodic and Many-Body Localized Systems
• Localizable quantum coherence
• Entanglement and area law with a fractal boundary in a topologically ordered phase
• Bounded light cone and robust topological order out of equilibrium