 Though the example of spin-\(\frac{1}{2}\) particles in the singlet state is ubiquitous in the literature as an illustrative example, polarization-entangled photons have been more significant for experimental tests of Bell inequalities. Consider a pair of photons 1 and 2 propagating in the \(z\)-direction. Let \(|x\rangle_j\) and \(|y\rangle_j\) represent states in which photon \(j \; (j =1, 2)\) is linearly polarized in the \(x\)- and \(y\)- directions, respectively. Consider the following state vector,