# How to find density matrix?

The Beam-splitter matrix is $B = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1\\ 1 & -1 \end{pmatrix}$.

I want to apply $a^{\dagger}_{1}a^{\dagger}_{2} |00\rangle_{12}$ as the input state for beam-splitter (two photon at two input ports).

How can i find density matrix for this state?

Density matrix of input state for one photon at one of two ports is(if my understanding is correct) $$\rho = |\Psi\rangle \langle\Psi| = \begin{pmatrix} 1 \\ 0 \end{pmatrix} \begin{pmatrix} 1 & 0 \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix}.$$

• If I understand well, here you find this same computation: en.wikipedia.org/wiki/… – Antonio Ragagnin Mar 31 '14 at 8:18
• this computation isn't using density matrix. – user_user Mar 31 '14 at 11:00