No, two quantum states interacting via quantum interactions do not always become entangled. The entanglement of two quantum states depends on the specific nature of the interaction and the initial states of the particles involved.
In quantum mechanics, when two or more quantum systems interact, their states can become entangled if the interaction couples their degrees of freedom in a way that leads to correlations between them. This entanglement arises when the joint state of the systems cannot be expressed as a product of individual states for each system.
However, not all interactions lead to entanglement. In some cases, the interaction may be such that the resulting joint state remains separable, meaning it can be expressed as a product of individual states. This occurs when the interaction does not generate correlations between the systems or when the systems are initially in states that are already uncorrelated.
The entanglement of quantum states is a complex and subtle phenomenon, and it depends on various factors, including the interaction strength, the initial states, and the specific details of the quantum systems involved. It is the interplay between these factors that determines whether entanglement emerges as a result of the interaction.