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 *Greenbergerâ€“Horneâ€“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.

*Daniel Greenberger (middle), Anton Zailinger (right); our diagram (background)*

*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.