Symmetry enforced entanglement in mixed states

          @misc{ scivideos_PIRSA:26050065,
            doi = {10.48660/26050065},
            url = {https://pirsa.org/26050065},
            author = {Sahu, Subhayan},
            keywords = {Quantum Information, Quantum Matter},
            language = {en},
            title = {Symmetry enforced entanglement in mixed states},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2026},
            month = {may},
            note = {PIRSA:26050065 see, \url{https://scivideos.org/pirsa/26050065}}
          }
          

Abstract

Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Strongly symmetric interactions, i.e. those that preserve a system's symmetry, however, can enforce non-trivial quantum entanglement patterns. We show that the highly mixed steady states of strongly symmetric unital quantum channels that preserve a non-Abelian symmetry are generically entangled. Remarkably, for non-Abelian continuous symmetries such as SU(2), the bipartite entanglement of formation scales logarithmically ∼ log N with the number of qudits N. Next, we show that such highly entangled steady states can also arise in models which exhibits quantum Hilbert space fragmentation. These states exhibit a surprising hierarchical entanglement structure, with volume-law negativity but sub-volume law entanglement of formation. Finally, we study strongly symmetric Gibbs states, or the canonical ensemble, at finite temperatures for generic local Hamiltonians with global on-site symmetries. Unlike the usual Gibbs state, we prove that the canonical ensemble remains entangled at all finite temperatures even for Abelian symmetries, and has no sudden death of entanglement.