The paper explores the entanglement properties of maximally mixed states in quantum many-body systems, particularly those with strong symmetry. For unital quantum channels that preserve a global on-site symmetry, the maximally mixed state (MMIS) in certain symmetry sectors can be highly entangled. The authors analyze the entanglement and correlations of the MMIS in the invariant sector (MMIS) and show that the entanglement of formation and distillation are exactly computable and equal for any bipartition. For Abelian symmetries, the MMIS is separable, while for non-Abelian symmetries, it is entangled. Notably, for non-Abelian continuous symmetries described by compact semisimple Lie groups (e.g., \(SU(2)\)), the bipartite entanglement of formation for the MMIS scales logarithmically with the number of qubits (\(\sim \log N\)). The paper also discusses the preparation and stability of MMIS, providing bounds on preparation time and demonstrating strong-to-weak spontaneous symmetry breaking (SSWB). The results highlight the interplay between symmetry and entanglement in quantum systems, showing that strong symmetry can enforce long-range entanglement in otherwise maximally mixed states.The paper explores the entanglement properties of maximally mixed states in quantum many-body systems, particularly those with strong symmetry. For unital quantum channels that preserve a global on-site symmetry, the maximally mixed state (MMIS) in certain symmetry sectors can be highly entangled. The authors analyze the entanglement and correlations of the MMIS in the invariant sector (MMIS) and show that the entanglement of formation and distillation are exactly computable and equal for any bipartition. For Abelian symmetries, the MMIS is separable, while for non-Abelian symmetries, it is entangled. Notably, for non-Abelian continuous symmetries described by compact semisimple Lie groups (e.g., \(SU(2)\)), the bipartite entanglement of formation for the MMIS scales logarithmically with the number of qubits (\(\sim \log N\)). The paper also discusses the preparation and stability of MMIS, providing bounds on preparation time and demonstrating strong-to-weak spontaneous symmetry breaking (SSWB). The results highlight the interplay between symmetry and entanglement in quantum systems, showing that strong symmetry can enforce long-range entanglement in otherwise maximally mixed states.