X-states from a finite geometric perspective

Colm Kelleher (1) , Frédéric Holweck (2) , Péter Lévay (3) , Metod Saniga (4)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 ICB - Laboratoire Interdisciplinaire Carnot de Bourgogne
3 MTA-BME Research Group of Technical Analytical Chemistry
4 Astronomical Institute of the Slovak Academy of Sciences

It is found that 15 different types of two-qubit X-states split naturally into two sets (of cardinality 9 and 6) once their entanglement properties are taken into account. We characterize both the validity and entangled nature of the X-states with maximally-mixed subsystems in terms of certain parameters and show that their properties are related to a special class of geometric hyperplanes of the symplectic polar space of order two and rank two. Finally, we introduce the concept of hyperplane-states and briefly address their non-local properties.

Mots clés: X-statesEntanglementNon-localityPoint-line geometryTwo-qubit operatorsSymplectic polar space

Domaines: Physique [physics]

Colm Kelleher, Frédéric Holweck, Péter Lévay, Metod Saniga. X-states from a finite geometric perspective. Results in Physics, 2021, 22, pp.103859. ⟨10.1016/j.rinp.2021.103859⟩. ⟨hal-03283167⟩