Entanglement dynamics of light's orbital angular momentum under a Lorentz boost

In this study, we report on the evolution of photonic orbital angular momentum (OAM) entanglement in inertial reference frames under a Lorentz boost, covering the general cases of zero and non-zero relative motion between observers of the entangled state. We find that entanglement undergoes significant changes that are observer dependent, asymptotically approaching a minimum at very large velocities close to the light cone from the viewpoint of the stationary observers in the rest frame, and degrading completely from the viewpoint of the moving observer. Our results, as demonstrated through entanglement metrics such as entanglement entropy and purity, show that OAM and OAM entanglement are observer dependent, raising pertinent questions on the invariance of such entangled states to spacetime transformations.