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I wonder if there's a tool available to draw platonic solids or other 3-D shapes inside a Bloch sphere. Here's an example I found on a research paper: enter image description here In my previous visualizations, I used the kaleidoscope package in Python to simulate time-evolution inside the Bloch sphere. I wonder if there's a tool I could draw 3-D shapes also. Thanks!

ZR-
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    I mean, the "Bloch sphere" is just a sphere, so aren't you just asking "can I draw platonic solids inside a sphere?"? Or do you mean some sort of expression for the quantum states corresponding to the vertices of a platonic solid inscribed in a sphere? – glS Aug 04 '21 at 23:27
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    @glS Thanks for the comment! I'll be generating quantum states corresponding to the vertices of 3D shapes. I could visualize the states as scatters or vectors on the Bloch sphere, but I don't know how can I connect those vertices (or which tools I could use), like the example diagram:) – ZR- Aug 04 '21 at 23:31
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    so you justmean how to draw those graphics really, regardless of the underlying interpretation as quantum states? Tbh I'm not sure that this is particularly OT in this site, but anyway, you can do this sort of thing pretty easily with Mathematica. E.g. Graphics3D[{[email protected], Sphere[], Dodecahedron[0.72]}] generates https://i.stack.imgur.com/Ejoku.png. Figuring out the expression for the vertices you can also easily highlight them. You can also have a look at https://mathematica.stackexchange.com/q/125985/27539 for how to draw a fancier Bloch sphere with MMA – glS Aug 04 '21 at 23:36
  • @glS Great, thanks! – ZR- Aug 04 '21 at 23:39
  • Could you please add a link to the paper you mentioned? I am wondering what is the interpretation and/or application of these special states. – Martin Vesely Aug 05 '21 at 10:36
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    @Martin Vesely Yeah of course! https://www.researchgate.net/publication/235572367_Derivation_and_experimental_test_of_fidelity_benchmarks_for_remote_preparation_of_arbitrary_qubit_states – ZR- Aug 05 '21 at 16:12
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    These are also relevant for rotation sensing with Majorana constellations; eg https://arxiv.org/abs/1612.06804, https://arxiv.org/abs/1002.2158, etc – Quantum Mechanic Aug 06 '21 at 02:56
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    also all of the examples here http://polarization.markus-grassl.de/index.html – Quantum Mechanic Aug 06 '21 at 02:58

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