Symmetry enforced entanglement in maximally mixed states

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 $\sim \log N$ with the number of qudits $N$.

17+8 pages, 7 figures

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Cited by in corpus (14)

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• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak
• Mixed-state phase transitions in spin-Holstein models
• Many-body quantum catalysts for transforming between phases of matter
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States
• Entanglement cost hierarchies in quantum fragmented mixed states
• Symmetry Properties of Quantum Dynamical Entropy
• Entanglement transitions in a boundary-driven open quantum many-body system
• Locally Purified Maximally Mixed States At Scale: Entanglement Pruning and Symmetries
• Holographic duality between bulk topological order and boundary mixed-state order
• Symmetry-enforced minimal entanglement and correlation in quantum spin chains
• Operator entanglement in $\mathrm{SU}(2)$-symmetric dissipative quantum many-body dynamics