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Geometric approach to entanglement quantification with polynomial measures

Regula, Bartosz; Adesso, Gerardo


Bartosz Regula


We show that the quantification of entanglement of any rank-2 state with any polynomial entanglement measure can be recast as a geometric problem on the corresponding Bloch sphere. This approach provides insight into the properties of entanglement and allows us to relate different polynomial measures to each other, simplifying their quantification. In particular, unveiling and exploiting the geometric structure of the concurrence for two qubits, we show that the convex roof of any polynomial measure of entanglement can be quantified exactly for all rank-2 states of an arbitrary number of qubits which have only one or two unentangled states in their range. We give explicit examples by quantifying the three-tangle exactly for several representative classes of three-qubit states. We further show how our methods can be used to obtain analytical results for entanglement of more complex states if one can exploit symmetries in their geometric representation.


Regula, B., & Adesso, G. (2016). Geometric approach to entanglement quantification with polynomial measures. Physical Review A, 94(2), Article 022324.

Journal Article Type Article
Acceptance Date Jul 28, 2016
Publication Date Aug 19, 2016
Deposit Date Aug 31, 2017
Publicly Available Date Aug 31, 2017
Journal Physical Review A
Print ISSN 2469-9926
Electronic ISSN 2469-9926
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 94
Issue 2
Article Number 022324
Public URL
Publisher URL


PhysRevA.94.022324.pdf (975 Kb)

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