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Half the entanglement in critical systems is distillable from a single specimen

R. Orus·J. I. Latorre·J. Eisert·M. Cramer
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Abstract

We establish that the leading critical scaling of the single-copy entanglement is exactly one half of the entropy of entanglement of a block in critical infinite spin chains in a general setting, using methods of conformal field theory. Conformal symmetry imposes that the single-copy entanglement for critical many-body systems scales as E_1(ρ_L)=(c/6) \log L- (c/6) (π^2/\log L) + O(1/L), where L is the number of constituents in a block of an infinite chain and c corresponds to the central charge. This proves that from a single specimen of a critical chain, already half the entanglement can be distilled compared to the rate that is asymptotically available. The result is substantiated by a quantitative analysis for all translationally invariant quantum spin chains corresponding to general isotropic quasi-free fermionic models. An analytic example of the XY model shows that away from criticality the above simple relation is only maintained near the quantum phase transition point.

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R. Orus, J. I. Latorre, J. Eisert, M. Cramer. 2006-07-15. Half the entanglement in critical systems is distillable from a single specimen. https://doi.org/10.1103/physreva.73.060303

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