Symmetry-Enforced Entanglement in Maximally Mixed States
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 sy...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-12-01
|
| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.5.040336 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846141219483156480 |
|---|---|
| author | Amin Moharramipour Leonardo A. Lessa Chong Wang Timothy H. Hsieh Subhayan Sahu |
| author_facet | Amin Moharramipour Leonardo A. Lessa Chong Wang Timothy H. Hsieh Subhayan Sahu |
| author_sort | Amin Moharramipour |
| collection | DOAJ |
| description | 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 with the number of qudits N. |
| format | Article |
| id | doaj-art-c1b67f8778054edc846e3cc9327c9906 |
| institution | Kabale University |
| issn | 2691-3399 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj-art-c1b67f8778054edc846e3cc9327c99062024-12-04T15:10:24ZengAmerican Physical SocietyPRX Quantum2691-33992024-12-015404033610.1103/PRXQuantum.5.040336Symmetry-Enforced Entanglement in Maximally Mixed StatesAmin MoharramipourLeonardo A. LessaChong WangTimothy H. HsiehSubhayan SahuEntanglement 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 with the number of qudits N.http://doi.org/10.1103/PRXQuantum.5.040336 |
| spellingShingle | Amin Moharramipour Leonardo A. Lessa Chong Wang Timothy H. Hsieh Subhayan Sahu Symmetry-Enforced Entanglement in Maximally Mixed States PRX Quantum |
| title | Symmetry-Enforced Entanglement in Maximally Mixed States |
| title_full | Symmetry-Enforced Entanglement in Maximally Mixed States |
| title_fullStr | Symmetry-Enforced Entanglement in Maximally Mixed States |
| title_full_unstemmed | Symmetry-Enforced Entanglement in Maximally Mixed States |
| title_short | Symmetry-Enforced Entanglement in Maximally Mixed States |
| title_sort | symmetry enforced entanglement in maximally mixed states |
| url | http://doi.org/10.1103/PRXQuantum.5.040336 |
| work_keys_str_mv | AT aminmoharramipour symmetryenforcedentanglementinmaximallymixedstates AT leonardoalessa symmetryenforcedentanglementinmaximallymixedstates AT chongwang symmetryenforcedentanglementinmaximallymixedstates AT timothyhhsieh symmetryenforcedentanglementinmaximallymixedstates AT subhayansahu symmetryenforcedentanglementinmaximallymixedstates |