Talk:Quantum tomography

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proposual for section on photonic state tomography and introductory example
Dear fellow Wikipedians,

on my research on this topic I stumbled upon a 'more visual' explanation (Quantum State Tomography of the 6 qubit photonic symmetric Dicke State by Niggebaum) (page 16) on quantum tomography. The author describes quantum tomography measurements of photons, by first introducing the representation of a the state of a single photon on a bloch sphere. Then the vector S that describes the position inside or on the bloch sphere can be determined by repediately applying a projective measurement (polarizer and photodetector) in only one direction of the bloch sphere $$\hat{p} = \frac{1}{2}\cdot \left(\sigma_0 + \sigma_x \right) $$. To get the components of the S-vector, one rotates the bloch sphere with lambda/4 or lambda/2 plates. Following this one can see that 4 measurements need to be done, 3 to determine the components of the vector along the sigma_x,y,z direction and 1 for normalization purposes. Maybe some part of this explanation could be included as introduction to this article, since the Bloch sphere is mentioned in the "Problems with maximum likelihood estimation"-section.

Also I found it nontrivial to actually calculate how to get from the measurements of the probabilities for specific events to the density matrix in the case of multiple entangled states. This publication (PHOTONIC STATE TOMOGRAPHY by ALTEPETER) describes how one can calculate (page 127+128) the density matrix or bloch vector S from different measurements, while this paper includes the calculated matrices which relate the measurements with the density matrix. I think this is equivalent to the already existing section "Linear inversion" but I'm not sure.

Because I needed the matrices for other initial states I've written some python code to, as a first step reproduce the matrices from said paper: https://gist.github.com/userx14/a3a10eed77c1a4a2b2a827eed6c3aab8. Would a pseudocode version of this suit this page?

Maybe one could create a secion for photonic state tomography to include these proposuals?

Best Benjamin (19.11.2021 - 22:08 GMT + 1)