2. (12 pts: 2 per part) Consider a pair of photons 1 and 2, in the state |V): = |HV)+|VH) √2 (1) where |H) and |V) represent horizontal and vertical polarization as usual. (a) Calculate the probability to find the second photon vertically polarized. (b) If the second photon is found to be vertically polarized, what is the probability that the first one is vertically polarized? (c) If the second photon is found to be vertically polarized, calculate the probability of finding the first photon to be diagonally polarized (D) = (|H) + |V)) /√√2). (d) Use the projection postulate to find the state of the second photon if the first photon is measured to be diagonally polarized. (e) Calculate the probability of finding the photon pair to be in the Bell singlet state (the state we discussed in the context of the EPR "paradox"). (f) Is ) a product state or an entangled state? Prove your assertion.