When moving from configuration I into the avoided crossing of configuration II infinitely slow adiabatically, the probability of a transition from the \( \vert 01\rangle \) to the \( \vert 10\rangle \) state is zero according to the adiabatic theorem.
An infinitely fast shift in configuration will instead cause the transition probability to be 1. Changing configuration with a finite speed will thus result in a transition probability between one and zero, and hence an entangled state. In our system we have that logical states \( \vert 01\rangle \) to the \( \vert 10\rangle \) correspond to the two first excited states.