(7.5) Photon density matrices. (Quantum) 3
Write the density matrix for a vertically polarized photon $|V\rangle$ in the basis where $|V\rangle = \begin{pmatrix} 1\\0 \end{pmatrix}$ and a horizontal photon $|H\rangle = \begin{pmatrix} 0\\1 \end{pmatrix}$. Write the density matrix for a diagonally polarized photon, $\begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \end{pmatrix}$, and the density matrix for unpolarized light (note 2 on p. 136). Calculate Tr$\rho$, Tr$\rho^2$, and $S = -k_B$Tr$\rho \log \rho$. Interpret the values of the three traces physically. (Hint: One is a check for pure states, one is a measure of information, and one is a normalization.)
