According to our current understanding of quantum mechanics, if one entangled particle were to travel to another galaxy or any arbitrary distance away, the entanglement between the two particles would still persist. The distance between the particles does not affect the entanglement itself.
Entanglement is a fundamental property of quantum systems that transcends physical distance. When two particles become entangled, their states become intertwined, and measurements made on one particle instantaneously affect the state of the other, regardless of the spatial separation between them.
This instantaneous correlation, sometimes referred to as "spooky action at a distance," has been experimentally verified through tests of Bell's inequality and various entanglement experiments.
Therefore, if one particle from an entangled pair were to travel to another galaxy, it would remain entangled with its counterpart back on Earth. Any measurement made on one particle would still have an immediate impact on the state of the other particle, regardless of the vast distance between them.
However, it's worth noting that maintaining and detecting entanglement over large distances can be challenging due to the potential for interactions with the environment or other particles. Environmental factors can cause decoherence, which can disrupt or degrade the entanglement. Over extremely large distances, practical challenges such as signal degradation and communication limitations may also come into play.
Nonetheless, in principle, the entanglement itself is not affected by the spatial separation between the entangled particles.