A system's wave function is uniquely determined by its underlying physical state

Understand

We address the question of whether the quantum-mechanical wave function $\Psi$ of a system is uniquely determined by any complete description $\Lambda$ of the system's physical state.

• We show that this is the case if the latter satisfies a notion of "free choice".
• This notion requires that certain experimental parameters---those that according to quantum theory can be chosen independently of other variables---retain this property in the presence of $\Lambda$.
• An implication of this result is that, among all possible descriptions $\Lambda$ of a system's state compatible with free choice, the wave function $\Psi$ is as objective as $\Lambda$.