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Aren't the <x| forms usually called the "bras" and the |x> forms the "kets?" Or do you have them swapped on purpose?
yes, they are the same things in Wolfram quantum framework. Where you are referring to in this notebook (with potential mistake)?
The statement above the very first gray left-pointing triangle calls it a 'ket" if I read it correctly. The very first right-pointing symbol also seems to be called a "bra."
That's state representation in a quantum circuit diagram (eg similar to gates etc). The motivation to pick a triangle is to have similar icons/pictures like quantum processes/diagrammatic approach. The state's Dirac notation is also shown inside that gray triangle.
The Dirac notation can be also obtained as TraditionalForm of a quantum state. Look at this notebook for more details:
Thank you! I missed the little ket inside the triangle pointing the opposite way. Forgive me.