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(a) Give a mathematical criterion that can be used to decide whether a given two-photon polarization state is entangled or not. Illustrate your answer by explaining whether the following states are entangled: = (VV) + |VH)) |D) = (VV) + |HH)) √2 where the positional convention is used and [V) and H) represent vertical and horizontal polarization states relative to the z-axis. (b) The kets |Vo) = cos 0V) + sin |H) and H₂) = sin 0|V) + cos |H) represent states of vertical and horizontal polarization relative to an axis in the direction defined by the polar angle and the azimuthal angle = 0. Suppose that observer A measures the polarization of photon 1 relative to the axis with = 0₁, while observer B measures the polarization of photon 2 relative to the axis with 0 0₂. Express the kets |V0₁ V0₂) and Ho, Ho₂) in terms of |VV), [VH), HV) and HH).