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.
Mixed-State Quantum Anomaly and Multipartite Entanglement
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Nonreciprocity combined with open boundaries and symmetry defects produces a domain-wall traveling-wave phase and anomalous chiral relaxation in open quantum systems.
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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.
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Nonreciprocity-enriched steady phases in open quantum systems
Nonreciprocity combined with open boundaries and symmetry defects produces a domain-wall traveling-wave phase and anomalous chiral relaxation in open quantum systems.