2004/12/31 by F. Benatti, F Benatti, B. C. Hiesmayr +3
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum Information and Cryptography #Quantum many-body systems #quant-ph
paper · pdf · doi:10.1209/epl/i2005-10204-2
published as Eur.Phys. Lett. 72 (1), 28 (2005) · 7 pages, 2 figures, to be published in Eur.Phys.Lett
arxiv created 2005/08/03 · openalex publication_date 2005/09/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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 (Klümper A., Schadschneider A. and Zittartz J., J. Phys. A , 24 (1991) L955; Z. Phys. B , 87 (1992) 281; Europhys. Lett. , 24 (1993) 293). We study the entanglement properties of such states by means of their finitely correlated structure (Fannes M., Nachtergaele B. and Werner R. F., Comm. Math. Phys. , 144 (1992) 443; Europhys. Lett. , 10 (1989) 633; J. Phys. A , 24 (1991) L185). These states are recursively constructed by means of an auxiliary density matrix ρ on a matrix algebra ℬ and a completely positive map : ⊗ ℬ → ℬ, where is the spin 2 × 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 (Wootters W. K., Contemp. Math. , 305 (2002) 299) the entanglement shared between connected regions of the spin-chain. This range of possible applications is illustrated and the maximal concurrence = 1/√2 (Coffman V., Kundu J. and Wootters W. K., Phys. Rev. A , 61 (2000) 052306) for the entanglement of connected regions can actually be reached.