Hadley, C.; (2008) Single-copy entanglement in a gapped quantum spin chain. Physical Review Letters , 100 (17) 177202-1-177202-4.

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Abstract

The single copy entanglement of a given many-body quantum system is defined [1] as the maximal amount of entanglement entropy (equivalently, the maximal number of EPR singlets) one can deterministically distill from a bipartition of a single specimen of that system. For critical (gapless) quantum spin chains, it was recently shown that this is exactly half the von Neumann entropy [2], itself defined as the number of EPR singlets one can distill in the asymptotic limit—that is, 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 AKLT 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. This appears to a simple explanation in terms of the valence bond solid representation of the state, but provides the first evidence that gapped spin chains also have different behaviour in the context of single copies as well as in the asymptotic limit. Calculations are performed using a coherent spin state representation, allowing straight-forward evaluation of properties through a transfer matrix approach.

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