Strong symmetries enforce nontrivial quantum entanglement patterns on the stationary states of symmetric open quantum dynamics. Specifically, noncommuting conserved quantities lead to long-range quantum entanglement even for infinite-temperature mixed states within fixed symmetry sectors. Leveraging the commutant algebra framework, we show that for any bipartition of such states, regardless of their geometry, various bipartite entanglement measures—including exact and asymptotically exact entanglement costs and squashed entanglement, which are generally intractable for a generic many-body mixed state—can be exactly computed. In particular, we focus on strongly symmetric maximally mixed states arising from the Temperley-Lieb model, which features quantum Hilbert-space fragmentation with exponentially large (in system size) non-Abelian commutants. We find that while both the logarithmic negativity and the "exact" entanglement cost for equal-size bipartitions scale with the volume of the system, the entanglement of formation, squashed entanglement, entanglement cost, and distillable entanglement exhibit subextensive scaling. We relate this separation in entanglement measures to a parametric difference between the entanglement costs of exact and asymptotically exact state preparations and infer it to be a consequence of a particular pattern of quantum Hilbert-space fragmentation.

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• Open quantum systems & decoherence
• Quantum coherence & coherence measures
• Quantum correlations in quantum information