\times \sin\frac{\vartheta_{N+1}}{2} \sin\frac{\vartheta_{N+2}}{2} \cdots \sin\frac{\vartheta_{n}}{2}   \nonumber  \\
&& \times e^{-i(z_{N+1}\varphi_{N+1}+z_{N+2}\varphi_{N+2}+ \cdots +
z_{n}\varphi_{n})}  \nonumber  \\
&& \times |-z_1\rangle |-z_2\rangle \cdots |-z_N\rangle \biggr] .\end{aligned}$$ Clearly, expressions (26) and (27) reduce to Eqs. (6a) and (5a), respectively, when we take $N=2$ and $n=3$. Similarly, by taking the partial trace of $|\Psi\rangle\langle\Psi|$ over the states corresponding to particles $N+1, N+2,\ldots, n,$ one finds that the reduced density matrix associated with the remaining $N$-particle system is $$\rho_{12 \cdots N} = c^2_1 |\phi^{+}_{12 \cdots N}\rangle\langle \phi^{+}_{12 \cdots N}|
+ c^2_2 |\phi^{-}_{12 \cdots N}\rangle\langle \phi^{-}_{12 \cdots N}| ,$$ with $|\phi^{+}_{12 \cdots N}\rangle$ and $|\phi^{-}_{12 \cdots N}\rangle$ being $|z_1\rangle
|z_2\rangle \cdots |z_N\rangle$ and $|-z_1\rangle |-z_2\rangle \cdots |-z_N\rangle$, respectively. This implies that no violation of local realism can result from joint measurements performed on particles $1,2,\ldots,N$ alone if such measurements are made without any commitment to the results obtained for particles $N+1,N+2,\ldots,n$ (as a matter of fact, no actual measurements need to be performed on particles $N+1,N+2,\ldots,n$ if we are looking at the unconditional correlation function for particles $1,2,\ldots,N,$ since this latter is, by definition, fully independent of whatever measurements on particles $N+1,N+2,\ldots,n$). Indeed, it is not difficult to show that the quantum prediction for the unconditional correlation 