Single-copy entanglement in a gapped quantum spin chain

Abstract

The single-copy entanglement of a given many-body system is defined [J. Eisert and M. Cramer, Phys. Rev. A. 72, 042112 (2005)] as the maximal entanglement deterministically distillable from a bipartition of a single specimen of that system. For critical (gapless) spin chains, it was recently shown that this is exactly half the von Neumann entropy [R. Orus, J. I. Latorre, J. Eisert, and M. Cramer, Phys. Rev. A 73, 060303(R) (2006)], itself defined as the entanglement distillable in the asymptotic limit: i.e. given an infinite number of copies of the system. It is an open question as to what the equivalent behaviour for gapped systems is. In this paper, I show that for the paradigmatic spin-S Affleck-Kennedy-Lieb-Tasaki chain (the archetypal gapped chain), the single-copy entanglement is equal to the von Neumann entropy: i.e. all the entanglement present may be distilled from a single specimen.

Typos corrected; accepted for publication in Phys. Rev. Lett.; comments welcome

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• Geometric Entanglement in a One-Dimensional Valence Bond Solid State
• Entanglement in valence-bond-solid states on symmetric graphs
• Entanglement of Valence-Bond-Solid on an Arbitrary Graph
• Extraction of Pure Entangled States from Many Body Systems by Distant Local Projections
• Effective thermodynamics of isolated entangled squeezed and coherent states
• Maximized string order parameters in the valence bond solid states of quantum integer spin chains