In general, we apply Bell's inequality in the context of two entangled particles that travel away from each other, usually making some measurements in a non-separable state that can be describes as:
$| \psi \rangle=|\uparrow\rangle|\downarrow\rangle-|\downarrow\rangle|\uparrow\rangle$ where the first bracket on each term corresponds to one particle, and the second to the other.
But I could not find any assumption in the derivation that stops us from applying the inequality to a single particle state, also described by a state like the one above, but in which the first and second brackets represent two different observables on the same particle, let us say spin and angular momentum (assuming they are not coupled).
Is this correct? will these measurements on a single particle also violate Bell's inequality? If this is so, can we still argue that a possible reason for the violation of the inequality is non-locality, due to the fact that the two measurements are local?
UPDATE: After the original post I found this, which seems to answer my question.