(See also https://cmp.felk.cvut.cz/~navara/lectures/SvozilN_Abstract.html)

In quantum physics, so-called entangled quantum states play an important role.
Quantum entanglement occurs when a group of particles interact in such a way
that the quantum state of each particle of the group cannot be described
independently of the state of the others.
A famous one is the Greenberger–Horne–Zeilinger state.

We studied a diagram related to entanglement, which has specific properties.•
To prove that such a configuration is realistic, we had to show that it is the
orthogonality diagram of a real set of vectors in 3D.
We accomplished this in a joint work with Karl Svozil from TU Wien.

We used only elements of 3D geometry, thus the topic can be understood also by
a wider audience not necessarily familiar with quantum logics.

•For insiders:
The diagram represents a quantum logic (orthomodular lattice) with elements a,
b, c, d, e, f such that, for any probability measure P, we have
P(a)+P(b)+P(c) = P(d)+P(e)+P(f),
while this sum can be almost arbitrary.