The distance between two quantum-entangled particles is not limited in any way. Quantum entanglement is a phenomenon in which two or more particles become correlated in such a way that the state of one particle is dependent on the state of the other(s), regardless of the distance between them. This correlation persists regardless of the physical separation between the entangled particles.
The entangled particles can be separated by vast distances, even across the entire universe, and their entangled state remains intact. Changes made to one particle's state instantaneously affect the state of the other particle, regardless of the spatial separation.
This seemingly non-local connection between entangled particles is known as "spooky action at a distance," as famously described by Albert Einstein. It violates the classical concept of locality, where information cannot travel faster than the speed of light. However, it is important to note that this non-locality does not allow for faster-than-light communication or transmission of information, as exploiting entanglement for communication violates the principles of causality and information causality.
In practice, the entanglement of particles can be achieved through various methods such as the creation of entangled pairs through specific quantum processes or by extracting entanglement from larger entangled systems. Once entangled, the particles can be separated and studied individually, while their entangled state is maintained.