Entanglement quantification made easy: polynomial measures invariant under convex decomposition
Quantifying entanglement in composite systems is a fundamental challenge, yet exact results are only available in few special cases. This is because hard optimization problems are routinely involved, such as finding the convex decomposition of a mixed state with the minimal average pure-state entang...
| 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/40794/ |
| _version_ | 1848796134897614848 |
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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 | Quantifying entanglement in composite systems is a fundamental challenge, yet exact results are only available in few special cases. This is because hard optimization problems are routinely involved, such as finding the convex decomposition of a mixed state with the minimal average pure-state entanglement, the so-called convex roof. We show that under certain conditions such a problem becomes trivial. Precisely, we prove by a geometric argument that polynomial entanglement measures of degree 2 are independent of the choice of pure-state decomposition of a mixed state, when the latter has only one pure unentangled state in its range. This allows for the analytical evaluation of convex roof extended entanglement measures in classes of rank-two states obeying such condition. We give explicit examples for the square root of the three-tangle in three-qubit states, and show that several representative classes of four-qubit pure states have marginals that enjoy this property. |
| first_indexed | 2025-11-14T19:43:10Z |
| format | Article |
| id | nottingham-40794 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:43:10Z |
| publishDate | 2016 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-407942020-05-04T17:36:26Z https://eprints.nottingham.ac.uk/40794/ Entanglement quantification made easy: polynomial measures invariant under convex decomposition Regula, Bartosz Adesso, Gerardo Quantifying entanglement in composite systems is a fundamental challenge, yet exact results are only available in few special cases. This is because hard optimization problems are routinely involved, such as finding the convex decomposition of a mixed state with the minimal average pure-state entanglement, the so-called convex roof. We show that under certain conditions such a problem becomes trivial. Precisely, we prove by a geometric argument that polynomial entanglement measures of degree 2 are independent of the choice of pure-state decomposition of a mixed state, when the latter has only one pure unentangled state in its range. This allows for the analytical evaluation of convex roof extended entanglement measures in classes of rank-two states obeying such condition. We give explicit examples for the square root of the three-tangle in three-qubit states, and show that several representative classes of four-qubit pure states have marginals that enjoy this property. American Physical Society 2016-02-19 Article PeerReviewed Regula, Bartosz and Adesso, Gerardo (2016) Entanglement quantification made easy: polynomial measures invariant under convex decomposition. Physical Review Letters, 116 . 070504/1-070504/5. ISSN 1079-7114 http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.070504 doi:10.1103/PhysRevLett.116.070504 doi:10.1103/PhysRevLett.116.070504 |
| spellingShingle | Regula, Bartosz Adesso, Gerardo Entanglement quantification made easy: polynomial measures invariant under convex decomposition |
| title | Entanglement quantification made easy: polynomial measures invariant under convex decomposition |
| title_full | Entanglement quantification made easy: polynomial measures invariant under convex decomposition |
| title_fullStr | Entanglement quantification made easy: polynomial measures invariant under convex decomposition |
| title_full_unstemmed | Entanglement quantification made easy: polynomial measures invariant under convex decomposition |
| title_short | Entanglement quantification made easy: polynomial measures invariant under convex decomposition |
| title_sort | entanglement quantification made easy: polynomial measures invariant under convex decomposition |
| url | https://eprints.nottingham.ac.uk/40794/ https://eprints.nottingham.ac.uk/40794/ https://eprints.nottingham.ac.uk/40794/ |