Density operator quantum mechanics

[pere]

I have the following situation: About the polarization of the photon, I introduce the basis:

Horizontal polarization $|\leftrightarrow>=\binom{1}{0}$
Vertical polarization $|\updownarrow>=\binom{0}{1}$

The density matrix in this problem is:

$$\rho =\frac{1}{2}\begin{pmatrix}
1+\xi _{1} & \xi_{2}-i\xi _{3}\\
\xi_{2}+i\xi _{3} & 1-\xi _{1}
\end{pmatrix}$$

The Stokes parameters are: $\xi _{1}, \xi _{2}, \xi _{3}$

The probability that if the photon has got lineal polarization whose axis forms an angle $\theta$ with de horizontal is:

$$|w>=cos\theta |\leftrightarrow>+sin\theta|\updownarrow>$$

$$ P_{\theta}=<w|\rho|w>=\frac{1}{2}\left ( 1+\xi_{1}cos(2\theta)+\xi_{2}sin(2\theta) \right )$$

Is there any value of the [Stokes parameters](http://en.wikipedia.org/wiki/Stokes_parameters) for which this probability is zero?

 

[Nate810]

Yes, there is a value of the Stokes parameters for which the probability is zero. Specifically, if $\xi_1 = -1$ and $\xi_2 = \sin(2\theta)$, then $P_\theta = 0$.