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Entanglement quantification made easy: polynomial measures invariant under convex decomposition

Regula, Bartosz; Adesso, Gerardo

Authors

Bartosz Regula



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 Feb 24, 2017
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

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