According to the principles of quantum mechanics, when two particles are entangled, their quantum states become correlated in such a way that the state of one particle is dependent on the state of the other. This entanglement can persist even after a measurement is performed on one of the particles. However, the measurement does have an effect on the entangled system.
When a measurement is made on an entangled particle, it "collapses" the quantum state of that particle into a specific eigenstate of the measured property. This collapse is random and unpredictable, following the probabilities defined by the wavefunction. As a result, the entangled state of the other particle instantaneously changes as well, ensuring the overall correlation between the two particles.
After the measurement, the entangled particles may still exhibit correlations in subsequent measurements of other properties. These correlations can persist even if the particles are physically separated. This phenomenon is known as non-locality, where the state of one particle appears to have an instant effect on the state of the other, regardless of the distance between them.
However, it is important to note that once a measurement is performed on one of the entangled particles, the entanglement cannot be used for faster-than-light communication or transfer of information. The collapse of the quantum state and the subsequent correlations are probabilistic and do not allow for direct control or manipulation of information.
In summary, entanglement can persist between particles even after measurement, but the act of measurement affects the entangled system by collapsing the quantum states and modifying the correlations between the particles.