# Polarization of light using Mueller matrix

Hi everyone
First of all, I am a computer science student and I have a question regarding the polarization of light as stated in an article entitled "Multi-stage quantum secure communication using polarization hopping" by Rifai et al.,2015.
Given the Mueller matrix:

The input of light state is:

And lastly, the operation to produce the output of light after it go through a half wave plate:

After I do the calculation, the S_out for the θx=0° is [1 1 0 0] meaning that the light is horizontally polarized. However, when the θx=45°, I didn't get the vertical light polarization [1 -1 0 0] as stated in wikipedia:

This is the result of my calculation using Python programming language:

It seems that my vertical polarization of light is wrong. I hope that anyone may help me to clarify this problem.
Thank you so much & regards.

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Hi everyone
First of all, I am a computer science student and I have a question regarding the polarization of light as stated in an article entitled "Multi-stage quantum secure communication using polarization hopping" by Rifai et al.,2015.

I did a quick read of the paper, and I'm a little confused by the parameter 'θx'. How does θx relate to θA and/or θB (referring to Figure 3)?

I did a quick read of the paper, and I'm a little confused by the parameter 'θx'. How does θx relate to θA and/or θB (referring to Figure 3)?
θA is the rotational of half wave plate at Alice side while θB is rotational at Bob and they are unitary transformation.