Europhys. Lett.
Volume 72, Number 1, October 2005
Page(s) 28 - 34
Section General
Published online 02 September 2005
Europhys. Lett., 72 (1), pp. 28-34 (2005)
DOI: 10.1209/epl/i2005-10204-2

Multi-distributed entanglement in finitely correlated chains

F. Benatti1, 2, B. C. Hiesmayr3 and H. Narnhofer3

1  Dipartimento di Fisica Teorica, Università di Trieste Strada Costiera 11, 34014 Trieste, Italy
2  Istituto Nazionale di Fisica Nucleare, Sezione di Trieste - 34100 Trieste, Italy
3  Institut für Theoretische Physik - Boltzmanngasse 5, A-1090 Vienna, Austria

received 14 April 2005; accepted in final form 2 August 2005
published online 2 September 2005

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 $\rho$ on a matrix algebra $\mathcal{B}$ and a completely positive map $\mathbb{E} :\mathcal{A} \otimes \mathcal{B}\to\mathcal{B}$, where $\mathcal{A}$ 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 (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 $\mathcal{C}=\frac{1}{\sqrt{2}}$ (COFFMAN V., KUNDU J. AND WOOTTERS W. K., Phys. Rev. A, 61 (2000) 052306) for the entanglement of connected regions can actually be reached.

03.67.Mn - Entanglement production, characterization, and manipulation.
05.50.+q - Lattice theory and statistics (Ising, Potts, etc.).

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