Framework for classifying logical operators in stabilizer codes
Entanglement, as studied in quantum information science, and nonlocal quantum correlations, as studied in condensed matter physics, are fundamentally akin to each other. However, their relationship is often hard to quantify due to the lack of a general approach to study both on the same footing. In...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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American Physical Society
2010
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| Online Access: | http://hdl.handle.net/1721.1/58779 https://orcid.org/0000-0001-7296-523X |
| _version_ | 1826188339632406528 |
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| author | Yoshida, Beni Chuang, Isaac L. |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Yoshida, Beni Chuang, Isaac L. |
| author_sort | Yoshida, Beni |
| collection | MIT |
| description | Entanglement, as studied in quantum information science, and nonlocal quantum correlations, as studied in condensed matter physics, are fundamentally akin to each other. However, their relationship is often hard to quantify due to the lack of a general approach to study both on the same footing. In particular, while entanglement and nonlocal correlations are properties of states, both arise from symmetries of global operators that commute with the system Hamiltonian. Here, we introduce a framework for completely classifying the local and nonlocal properties of all such global operators, given the Hamiltonian and a bipartitioning of the system. This framework is limited to descriptions based on stabilizer quantum codes, but may be generalized. We illustrate the use of this framework to study entanglement and nonlocal correlations by analyzing global symmetries in topological order, distribution of entanglement, and entanglement entropy. |
| first_indexed | 2024-09-23T07:58:09Z |
| format | Article |
| id | mit-1721.1/58779 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T07:58:09Z |
| publishDate | 2010 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/587792022-09-23T09:58:05Z Framework for classifying logical operators in stabilizer codes Yoshida, Beni Chuang, Isaac L. Massachusetts Institute of Technology. Department of Physics Chuang, Isaac L. Yoshida, Beni Chuang, Isaac L. Entanglement, as studied in quantum information science, and nonlocal quantum correlations, as studied in condensed matter physics, are fundamentally akin to each other. However, their relationship is often hard to quantify due to the lack of a general approach to study both on the same footing. In particular, while entanglement and nonlocal correlations are properties of states, both arise from symmetries of global operators that commute with the system Hamiltonian. Here, we introduce a framework for completely classifying the local and nonlocal properties of all such global operators, given the Hamiltonian and a bipartitioning of the system. This framework is limited to descriptions based on stabilizer quantum codes, but may be generalized. We illustrate the use of this framework to study entanglement and nonlocal correlations by analyzing global symmetries in topological order, distribution of entanglement, and entanglement entropy. 2010-09-30T14:40:15Z 2010-09-30T14:40:15Z 2010-05 2010-01 Article http://purl.org/eprint/type/JournalArticle 1050-2947 1094-1622 http://hdl.handle.net/1721.1/58779 Yoshida, Beni, and Isaac L. Chuang. "Framework for classifying logical operators in stabilizer codes." Physical Review A 81.5 (2010): 052302. © 2010 The American Physical Society https://orcid.org/0000-0001-7296-523X en_US http://dx.doi.org/10.1103/PhysRevA.81.052302 Physical Review A Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Yoshida, Beni Chuang, Isaac L. Framework for classifying logical operators in stabilizer codes |
| title | Framework for classifying logical operators in stabilizer codes |
| title_full | Framework for classifying logical operators in stabilizer codes |
| title_fullStr | Framework for classifying logical operators in stabilizer codes |
| title_full_unstemmed | Framework for classifying logical operators in stabilizer codes |
| title_short | Framework for classifying logical operators in stabilizer codes |
| title_sort | framework for classifying logical operators in stabilizer codes |
| url | http://hdl.handle.net/1721.1/58779 https://orcid.org/0000-0001-7296-523X |
| work_keys_str_mv | AT yoshidabeni frameworkforclassifyinglogicaloperatorsinstabilizercodes AT chuangisaacl frameworkforclassifyinglogicaloperatorsinstabilizercodes |