According to our current understanding of quantum mechanics and the theory of general relativity, if two quantum-entangled particles are separated and one of them crosses the event horizon of a black hole, the entanglement between them would be disrupted or lost.
When particles are entangled, their quantum states are correlated in a way that the measurement of one particle's state instantaneously affects the state of the other particle, regardless of the distance between them. This phenomenon, known as quantum entanglement, is a fundamental aspect of quantum mechanics.
However, once a particle crosses the event horizon of a black hole, it is no longer accessible from outside the black hole. General relativity predicts that information and particles that enter a black hole are trapped within the black hole's singularity, and they cannot escape or be observed from the outside. Therefore, any entanglement between the particle inside the black hole and its entangled partner outside the black hole would effectively be lost.
This scenario poses a significant challenge known as the "information paradox." According to quantum mechanics, information is always conserved, and the loss of information due to the destruction of entanglement violates this principle. Resolving this paradox is an active area of research, and various proposals, such as the holographic principle and black hole evaporation through Hawking radiation, have been suggested to reconcile quantum mechanics and general relativity in the context of black holes.
In summary, based on our current understanding, the crossing of the event horizon by one entangled particle into a black hole would disrupt or break the entanglement between the particles. The exact fate of the information and the resolution of the information paradox in the presence of black holes remain topics of ongoing scientific investigation.