Past exam of the laser science and quantum information processing course of the University of Oxford / 2009 / 8 / 1 / Solution

Normalize the supplied Bell state as $|{\Psi }^{+}⟩=(|01⟩+|10⟩)/\sqrt{2}$, with $|V⟩=|0⟩$ and $|H⟩=|1⟩$. For a measurement of linear photon polarization, the two orthogonal analyzer states can be taken asAssigning outcomes $+1,-1$ gives the observablewhere $X,Z$ are the Pauli operators. The angle of the Bloch vector is twice the physical analyzer angle. HenceEach has eigenvalues $\pm 1$ and square equal to the identity operator.