In quantum mechanics, entanglement refers to a phenomenon where the quantum states of two or more particles become correlated in such a way that the state of one particle cannot be described independently of the state of the other particles. When particles are entangled, their quantum states are said to be "entangled states" or "superposition states."
When entangled particles become separated by a distance, their entangled state does not change due to their spatial separation. This means that even if the particles are physically far apart, the entanglement between them persists. This characteristic is known as "non-locality" and is one of the intriguing aspects of quantum mechanics.
The entanglement between particles remains intact until some form of measurement or interaction takes place. When an observation or measurement is performed on one of the entangled particles, it affects the entangled state, and the entanglement between the particles can be "broken" or "collapsed." This collapse of the entangled state results in the particles having definite, non-entangled states.
However, it's important to note that the collapse of the entangled state on one particle does not instantaneously affect the state of the other particle. This is due to the non-local nature of entanglement, where the measurement outcome on one particle can be random and doesn't provide any information about the state of the other particle. The information about the measurement outcome propagates at most at the speed of light.
So, to answer your question, once particles become entangled, their entanglement generally persists even if they are separated by a distance. However, when measurements or interactions occur, the entanglement can be broken or altered, and the particles will no longer be entangled.