Symmetry enforced entanglement in maximally mixed states

• URL: http://arxiv.org/abs/2406.08542v2
• Date: Fri, 13 Dec 2024 09:23:09 GMT
• Title: Symmetry enforced entanglement in maximally mixed states
• Authors: Amin Moharramipour, Leonardo A. Lessa, Chong Wang, Timothy H. Hsieh, Subhayan Sahu,
• Abstract summary: Entanglement in quantum many-body systems is typically fragile to interactions with the environment. We analyze the entanglement and correlations of the maximally mixed state in the invariant sector. For all Abelian symmetries, the MMIS is separable, and for all non-Abelian symmetries, the MMIS is entangled.
• Score: 3.5602863178766966
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• 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 $N$.

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