I struggle to see the difference between $|\Phi^+\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |0\rangle_B + |1\rangle_A \otimes |1\rangle_B)$ and the mixed state defined with probabilities {0.5, 0.5} and pure states $|00\rangle$ and $|11\rangle$.
In the case of a single qubit, it is easy to see the difference between $|+\rangle$ and the mixed state with probabilities {0.5, 0.5} and pure states $|0\rangle$ and $|1\rangle$ because when measured in the Z basis they behave the same (same probability distribution) but not in the X basis.
So what is the equivalent for Bell state?