The concept of entanglement and its measurement can indeed be counterintuitive. However, it's important to note that the act of measuring an entangled system does not necessarily destroy the entanglement itself. Let me explain further.
In quantum mechanics, when two or more particles are entangled, their states become correlated in such a way that the state of one particle cannot be described independently of the others. This entangled state is typically described using a mathematical construct known as a wave function.
To determine if particles are entangled, we perform measurements on their respective properties and observe the correlations between the outcomes. The measurement process does involve an interaction with the particles, which can change their states. This is known as wave function collapse or quantum decoherence.
However, it's important to understand that entanglement is not destroyed by the act of measurement or collapse of the wave function. Instead, the entangled state may evolve into a new entangled state due to the measurement interaction.
Once the measurement is performed, and the wave function collapses, the entangled particles may no longer be in a superposition of states, but the entanglement itself can persist. The correlations between the particles' properties that were observed during the measurement can provide evidence of their prior entanglement.
To summarize, while measuring an entangled system may alter its state, it doesn't necessarily destroy the entanglement itself. The correlations observed during measurements can provide strong evidence of entanglement, even though the wave function collapses in the process. Quantum mechanics provides a mathematical framework for describing and understanding these phenomena, and experimental results have repeatedly confirmed the existence of entanglement.