Polarization of light using Mueller matrix

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Discussion Overview

The discussion revolves around the polarization of light using a Mueller matrix, specifically in the context of a paper on quantum secure communication. Participants explore the relationship between different angles of rotation of a half wave plate and the resulting polarization states of light.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a calculation that yields a horizontally polarized light state for θx=0° but fails to achieve the expected vertical polarization for θx=45° as stated in external sources.
  • Another participant questions the relationship between the parameter θx and the angles θA and θB, which are associated with the half wave plates at different locations.
  • A later reply clarifies that θA and θB represent the rotations of the half wave plates at Alice's and Bob's sides, respectively, and are unitary transformations.
  • One participant successfully reproduces the expected vertical polarization for θx=45° and suggests verifying calculations by hand to identify discrepancies in the Python script used by the first participant.
  • The initial poster later acknowledges an error in their Python code that led to the incorrect result.

Areas of Agreement / Disagreement

Participants express differing results regarding the polarization states achieved through calculations, indicating that there is no consensus on the outcomes of the calculations presented. Some participants successfully reproduce the expected results while others encounter discrepancies.

Contextual Notes

There are unresolved issues regarding the calculations performed in Python, and the discussion highlights the dependence on the correct interpretation of parameters and transformations involved in the process.

Nur Ziadah
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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.
Given the Mueller matrix:
upload_2018-7-17_23-6-47.png

The input of light state is:
upload_2018-7-17_23-8-46.png

And lastly, the operation to produce the output of light after it go through a half wave plate:
upload_2018-7-17_23-10-37.png

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:
upload_2018-7-17_23-27-30.png

This is the result of my calculation using Python programming language:
upload_2018-7-17_23-24-43.png

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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Nur Ziadah said:
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)?
 
Andy Resnick said:
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.
 
Nur Ziadah said:
θA is the rotational of half wave plate at Alice side while θB is rotational at Bob and they are unitary transformation.

Ok, I read through the paper more carefully and was able to reproduce most of their equations. I did indeed get vertical polarization for θx=45°. I'm not sure why your Python script returned a different result. Try it by hand, leaving θx as a free parameter, then after you calculate Sout, put in different values for θx.
 
Andy Resnick said:
Ok, I read through the paper more carefully and was able to reproduce most of their equations. I did indeed get vertical polarization for θx=45°. I'm not sure why your Python script returned a different result. Try it by hand, leaving θx as a free parameter, then after you calculate Sout, put in different values for θx.

Finally I got the true result. Something mistakes happened in my Python codes. Anyway, thank you for your explanation.
 

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