I can usually work out whether CHSH inequality is violated when the observables that we are measuring and the state we are in is given explicitly, but I'm struggling with the generality of the question below.
Consider that a source emits two quantum particles; one to Alice and one to Bob. The particles are in a state of the form $$|\psi>=|v>|u>$$ where $|v>$ is a state in Alice's Hilbert space and $|u>$ is a state in Bob's. Show there are no choices of local quantum observables $A_1,A_2,B_1,B_2$ which violate the CHSH inequality. We assume that $A_1,A_2,B_1,B_2$ can only be $+1$ or $-1$.