Multi-distributed Entanglement in Finitely Correlated Chains

Details Multi-distributed Entanglement in Finitely Correlated Chains Multi-distributed Entanglement in Finitely Correlated Chains

2004-12-21

arxiv.org/abs/quant-ph/0412167v3

Eur.Phys. Lett. 72 (1), 28 (2005)

Physics

Quantum Physics

7 pages, 2 figures, to be published in Eur.Phys.Lett

Scientific paper

10.1209/epl/i2005-10204-2

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 \rho on 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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