If two particles are entangled, their states become correlated in such a way that measuring one particle can instantaneously affect the state of the other particle, regardless of the distance between them. This phenomenon is known as quantum entanglement.
If one of the entangled particles is annihilated by an anti-particle, the state of the remaining particle depends on the specific details of the entanglement and the interaction that caused the annihilation. Generally, the remaining particle's state would no longer be entangled with the annihilated particle.
The act of annihilation typically involves the particle and its corresponding anti-particle coming into contact and mutually annihilating each other, releasing energy in the process. This interaction can disrupt the entanglement between the particles. As a result, the state of the remaining particle would be independent and unrelated to the annihilation event.
However, it's important to note that the exact outcome would depend on the specific properties of the particles involved, the nature of their entanglement, and the details of the annihilation process. Quantum systems can exhibit complex behaviors, and without specific information about the particles and the interaction, it is difficult to provide a more detailed description of what would happen to the remaining particle.