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: 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
• Contract Date: Feb 24, 2017