Single-Copy Entanglement in a Gapped Quantum Spin Chain

The single-copy entanglement of a given many-body quantum system is defined [J. Eisert and M. Cramer, Phys. Rev. A 72, 042112 (2005)PLRAAN1050-294710.1103/PhysRevA.72.042112] 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. Orús, J. I. Latorre, J. Eisert, and M. Cramer, Phys. Rev. A 73, 060303(R) (2006)PLRAAN1050-2947], 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 behavior for gapped systems is. In this Letter, 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.