Entanglement quantification made easy: polynomial measures invariant under convex decomposition

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

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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.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/775809
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1103/PhysRevLett.116.070504
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Depositing User: Adesso, Gerardo
Date Deposited: 24 Feb 2017 09:24
Last Modified: 04 May 2020 17:36
URI: https://eprints.nottingham.ac.uk/id/eprint/40794

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