The maximally mixed state in the translation-invariant subspace of a 1D ring is long-range entangled because the dimension of translationally symmetric short-range entangled states grows polynomially while the full subspace grows exponentially.
Matrix product operator algebras II: phases of matter for 1D mixed states
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Mixed-State Long-Range Entanglement from Dimensional Constraints
The maximally mixed state in the translation-invariant subspace of a 1D ring is long-range entangled because the dimension of translationally symmetric short-range entangled states grows polynomially while the full subspace grows exponentially.