# Density matrix for a diagonally polarized photon

I am struggling with the density matrix for diagonally polarized photons. Can I think of diagonally polarized photons as a mixture of vertically and horizontally polarized photons?

Yes, you can write a diagonally polarized state as a linear superposition of horizontally and vertically polarized states ("mixture" isn't the right term though; it's still a pure state). For instance, the $$45^{\circ}$$ diagonally polarized state $$\lvert \nearrow \rangle$$ may be expressed as $$\lvert \nearrow \rangle = \frac{1}{\sqrt 2} \lvert \rightarrow \rangle + \frac{1}{\sqrt 2}\lvert \uparrow \rangle.$$
The density matrix $$\rho$$ of this state can be written as $$\lvert\nearrow\rangle\langle \nearrow\rvert$$ (cf. this); try calculating the matrix notation by yourself.