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arXiv · 2008.03063

$X$-States From a Finite Geometric Perspective

Colm Kelleher·Frédéric Holweck·Péter Lévay·Metod Saniga
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Abstract

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.

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Colm Kelleher, Frédéric Holweck, Péter Lévay, Metod Saniga. 2020-08-07. $X$-States From a Finite Geometric Perspective. https://doi.org/10.1016/j.rinp.2021.103859

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