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arXiv:2509.22385

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

Moslem Mahdavifar

Published Sep 26, 2025• 0 citations

Abstract

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.

DOI: 10.48550/arxiv.2509.22385

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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.

Orbital angular momentum (OAM) as both classical and quantum states of light has proven essential in numerous applications, from high-capacity information transfer to enhanced precision and accuracy in metrology. Here, we extend OAM metrology to relativistic scenarios to determine the Lorentz factor of a moving reference frame, exploiting the fact that OAM is not Lorentz invariant. We show that the joint OAM spectrum from entangled states is modified by length contraction when measured by two observers moving relative to the entanglement source. This relative motion rescales the spatial dimensions, thus breaking the orthogonality of the OAM measurement process and resulting in a broadening of the joint OAM spectrum that can precisely determine the Lorentz factor. We experimentally simulate velocities up to

0.99c

, confirm the predicted broadening, and use the measurement outcomes to extract the Lorentz factor. Our work provides a pathway for novel measurement techniques suitable for relativistic conditions that leverage OAM structured light as a resource.

The orbital angular momentum (OAM) of photons has shown the ability to generate high-dimensional entanglement. Here, we examine a novel kind of entanglement degradation caused by the Unruh effect. By paraxially quantizing the light field, we derive the mode functions in both inertial and noninertial reference frames and demonstrate that, from the perspective of an accelerating observer, empty inertial space may seem to be full of OAM particles. They may inundate the high-dimensional entangled OAM photons and cause them to decay. Additionally, we investigate high-dimensional entanglement in the vicinity of a Schwarzschild black hole. Our results suggest that higher-dimensional entanglement will suffer from greater adverse impacts in both instances.

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