If two particles are in an entangled state and one of them undergoes annihilation or any other interaction, it does not instantaneously determine the state of the other particle. The state of the remaining particle will depend on the specific details of the interaction and the nature of the entangled state.
In quantum entanglement, the states of the two particles are intertwined in such a way that the measurement of one particle can instantaneously affect the state of the other particle, regardless of the distance between them. However, this instantaneous correlation does not imply that information or influence is transmitted faster than the speed of light. The correlation becomes apparent when measurements are made on both particles, revealing the entangled nature of their states.
If one particle undergoes annihilation, it means that it is no longer present or has interacted in a way that significantly alters its properties. The state of the remaining particle, which was entangled with the annihilated particle, will depend on the specific nature of the entanglement and the interaction that caused the annihilation.
In some cases, the entangled state may become "broken" or disentangled due to the interaction, and the remaining particle would then be in an independent state. In other cases, the entanglement may persist, but the measurement or interaction with the annihilated particle could alter the probabilities associated with the state of the remaining particle.
The precise outcome will depend on the specific experimental setup, the nature of the entanglement, and the details of the interaction. Without further information, it is difficult to provide a definitive answer about what happens to the remaining particle when one of the entangled particles undergoes annihilation.