Two particles begin their dance in complete independence. Neither knows of the other's existence. But under the invisible music of deformed spacetime, their motions gradually synchronize: entanglement is born in the system—that very quantum connection Einstein called 'spooky action at a distance.'

In the ordinary world, energies add up simply: take the energy of one particle, add the energy of the other, and you get the energy of the pair. But in κ-Minkowski spacetime (a space where coordinates do not commute), the law of energy addition is deformed. An extra term appears, proportional to the product of the particles' momenta. It acts as an invisible choreographer, causing the particles' states to intertwine.

But the same deformation of symmetries that creates entanglement also destroys it. Quantum spacetime behaves like a noisy environment: it constantly 'jostles' the particles, causing decoherence (loss of quantum properties). As a result, for all initial states except the maximally entangled one, entanglement disappears in a finite time. However, other quantum correlations—coherence (the ability to interfere) and mutual information (the total correlation between particles)—are preserved. The system does not collapse into classical chaos but remains in a delicate quantum equilibrium.

This work fills an important gap. Previously, it was known that quantum spacetime causes decoherence of single particles. But how it affects correlations between multiple particles remained unclear. Now it is clear: deformed symmetries not only destroy but also create quantum connections. Moreover, the mechanism of entanglement generation here is purely kinematic—it does not require physical interaction but arises from the modified energy addition law. This opens a new channel for experimental searches for traces of quantum gravity.

Experimentalists already know how to trap ions and maintain their quantum coherence for more than an hour. If entanglement born of deformed spacetime is detected in such a system, it would be the first direct evidence of the quantum nature of gravity. The dance of particles to the music of quantum spacetime may turn out to be not just a theoretical metaphor but an observable phenomenon.