Bartosz Regula
Entanglement quantification made easy: polynomial measures invariant under convex decomposition
Regula, Bartosz; Adesso, Gerardo
Abstract
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.
Citation
Regula, B., & Adesso, G. (2016). Entanglement quantification made easy: polynomial measures invariant under convex decomposition. Physical Review Letters, 116, Article 070504. https://doi.org/10.1103/PhysRevLett.116.070504
Journal Article Type | Article |
---|---|
Acceptance Date | Jan 21, 2016 |
Publication Date | Feb 19, 2016 |
Deposit Date | Feb 24, 2017 |
Publicly Available Date | Mar 28, 2024 |
Journal | Physical Review Letters |
Print ISSN | 0031-9007 |
Electronic ISSN | 1079-7114 |
Publisher | American Physical Society |
Peer Reviewed | Peer Reviewed |
Volume | 116 |
Article Number | 070504 |
DOI | https://doi.org/10.1103/PhysRevLett.116.070504 |
Public URL | https://nottingham-repository.worktribe.com/output/775809 |
Publisher URL | http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.070504 |
Related Public URLs | https://arxiv.org/abs/1512.03326 |
Files
1512.03326.pdf
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