PIRSA:24080002

Symmetry enforced entanglement in maximally mixed states

Sahu, S. (2024). Symmetry enforced entanglement in maximally mixed states. Perimeter Institute. https://pirsa.org/24080002

Sahu, Subhayan. Symmetry enforced entanglement in maximally mixed states. Perimeter Institute, Aug. 21, 2024, https://pirsa.org/24080002 

          @misc{ pirsa_PIRSA:24080002,
            doi = {10.48660/24080002},
            url = {https://pirsa.org/24080002},
            author = {Sahu, Subhayan},
            keywords = {Quantum Information},
            language = {en},
            title = {Symmetry enforced entanglement in maximally mixed states},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {aug},
            note = {PIRSA:24080002 see, \url{https://pirsa.org}}
          }

Subhayan Sahu

Perimeter Institute for Theoretical Physics

Talk number
PIRSA:24080002
Collection
Talk Type
Subject
Abstract

Entanglement in quantum many-body systems is typically fragile to interactions with the environment. Generic unital quantum channels, for example, have the maximally mixed state with no entanglement as their unique steady state. However, we find that for a unital quantum channel that is `strongly symmetric', i.e. it preserves a global on-site symmetry, the maximally mixed steady state in certain symmetry sectors can be highly entangled. For a given symmetry, we analyze the entanglement and correlations of the maximally mixed state in the invariant sector (MMIS), and show that the entanglement of formation and distillation are exactly computable and equal for any bipartition. For all Abelian symmetries, the MMIS is separable, and for all non-Abelian symmetries, the MMIS is entangled. Remarkably, 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 ∼logN with the number of qudits N.