Geometric approach to entanglement quantification with polynomial measures
We show that the quantification of entanglement of any rank-2 state with any polynomial entanglement measure can be recast as a geometric problem on the corresponding Bloch sphere. This approach provides insight into the properties of entanglement and allows us to relate different polynomial measure...
| Main Authors: | , |
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| Format: | Article |
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American Physical Society
2016
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| Online Access: | https://eprints.nottingham.ac.uk/45298/ |
| _version_ | 1848797107924762624 |
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| author | Regula, Bartosz Adesso, Gerardo |
| author_facet | Regula, Bartosz Adesso, Gerardo |
| author_sort | Regula, Bartosz |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We show that the quantification of entanglement of any rank-2 state with any polynomial entanglement measure can be recast as a geometric problem on the corresponding Bloch sphere. This approach provides insight into the properties of entanglement and allows us to relate different polynomial measures to each other, simplifying their quantification. In particular, unveiling and exploiting the geometric structure of the concurrence for two qubits, we show that the convex roof of any polynomial measure of entanglement can be quantified exactly for all rank-2 states of an arbitrary number of qubits which have only one or two unentangled states in their range. We give explicit examples by quantifying the three-tangle exactly for several representative classes of three-qubit states. We further show how our methods can be used to obtain analytical results for entanglement of more complex states if one can exploit symmetries in their geometric representation. |
| first_indexed | 2025-11-14T19:58:38Z |
| format | Article |
| id | nottingham-45298 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:58:38Z |
| publishDate | 2016 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-452982020-05-04T18:06:30Z https://eprints.nottingham.ac.uk/45298/ Geometric approach to entanglement quantification with polynomial measures Regula, Bartosz Adesso, Gerardo We show that the quantification of entanglement of any rank-2 state with any polynomial entanglement measure can be recast as a geometric problem on the corresponding Bloch sphere. This approach provides insight into the properties of entanglement and allows us to relate different polynomial measures to each other, simplifying their quantification. In particular, unveiling and exploiting the geometric structure of the concurrence for two qubits, we show that the convex roof of any polynomial measure of entanglement can be quantified exactly for all rank-2 states of an arbitrary number of qubits which have only one or two unentangled states in their range. We give explicit examples by quantifying the three-tangle exactly for several representative classes of three-qubit states. We further show how our methods can be used to obtain analytical results for entanglement of more complex states if one can exploit symmetries in their geometric representation. American Physical Society 2016-08-19 Article PeerReviewed Regula, Bartosz and Adesso, Gerardo (2016) Geometric approach to entanglement quantification with polynomial measures. Physical Review A, 94 (2). 022324/1-022324/12. ISSN 2469-9926 https://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.022324 doi:10.1103/PhysRevA.94.022324 doi:10.1103/PhysRevA.94.022324 |
| spellingShingle | Regula, Bartosz Adesso, Gerardo Geometric approach to entanglement quantification with polynomial measures |
| title | Geometric approach to entanglement quantification with polynomial measures |
| title_full | Geometric approach to entanglement quantification with polynomial measures |
| title_fullStr | Geometric approach to entanglement quantification with polynomial measures |
| title_full_unstemmed | Geometric approach to entanglement quantification with polynomial measures |
| title_short | Geometric approach to entanglement quantification with polynomial measures |
| title_sort | geometric approach to entanglement quantification with polynomial measures |
| url | https://eprints.nottingham.ac.uk/45298/ https://eprints.nottingham.ac.uk/45298/ https://eprints.nottingham.ac.uk/45298/ |