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Multi-distributed Entanglement in Finitely Correlated Chains

F. Benatti·B. C. Hiesmayr·H. Narnhofer
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Abstract

The entanglement-sharing properties of an infinite spin-chain are studied when the state of the chain is a pure, translation-invariant state with a matrix-product structure. We study the entanglement properties of such states by means of their finitely correlated structure. These states are recursively constructed by means of an auxiliary density matrix ρon a matrix algebra B and a completely positive map E: A \otimes B -> B, where A is the spin 2\times 2 matrix algebra. General structural results for the infinite chain are therefore obtained by explicit calculations in (finite) matrix algebras. In particular, we study not only the entanglement shared by nearest-neighbours, but also, differently from previous works, the entanglement shared between connected regions of the spin-chain. This range of possible applications is illustrated and the maximal concurrence C=1/\sqrt{2} for the entanglement of connected regions can actually be reached.

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F. Benatti, B. C. Hiesmayr, H. Narnhofer. 2005-08-03. Multi-distributed Entanglement in Finitely Correlated Chains. https://doi.org/10.1209/epl%2Fi2005-10204-2

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