According to the standard interpretation of quantum mechanics, when particles are measured and their quantum states collapse, the entanglement between them is typically considered to be broken. This is known as the "collapse of the wave function" or "decoherence."
When two particles are entangled, their quantum states are correlated in a way that measuring one particle's state instantly determines the state of the other particle, regardless of the distance between them. However, once a measurement is made on one of the entangled particles, its quantum state collapses into a definite value, breaking the entanglement.
The collapse of the wave function is a fundamental aspect of the Copenhagen interpretation of quantum mechanics, which is the most widely accepted interpretation among physicists. It suggests that the act of measurement causes the wave function to "collapse" to a specific outcome, which is one of the possible states of the system. This collapse is accompanied by the loss of entanglement.
However, it's important to note that there are alternative interpretations of quantum mechanics, such as the Many-Worlds interpretation and the Pilot-Wave theory, which propose different ways to explain the behavior of quantum systems. These interpretations may have different perspectives on the persistence of entanglement after measurement, but they are not as widely accepted as the Copenhagen interpretation.
In summary, according to the standard interpretation of quantum mechanics, entanglement is typically considered to be broken when particles are measured and their quantum states collapse.