New answers tagged notation
5
There are several, these are the ones I have seen:
$|+\rangle_y,|-\rangle_y$ a bit lazy but easy to remember
$|+i\rangle,|-i\rangle$ the same as before but you replace the sub index with an imaginary unit $i$
$|\circlearrowleft\rangle,|\circlearrowright\rangle$ this notation is borrowed from light polarization, as you can use photons for light too, circular ...
5
As the other answer mentioned, they are often denoted as
$$|+i\rangle= \dfrac{|0\rangle + i|1\rangle}{\sqrt{2}} = \dfrac{1}{\sqrt{2}} \begin{pmatrix} 1 \\ i\end{pmatrix} \ \ \ \textrm{and} \ \ \ |-i\rangle = \dfrac{|0\rangle - i|1\rangle}{\sqrt{2}} = \dfrac{1}{\sqrt{2}} \begin{pmatrix} 1 \\ -i\end{pmatrix} $$
but sometime you might also see them denoted as ...
2
They are commonly denoted as
$$
\left\{ |+i\rangle = \frac{|0\rangle + i|1\rangle}{\sqrt{2}}, |-i\rangle = \frac{|0\rangle - i|1\rangle}{\sqrt{2}}\right\}
$$
So, you could use $|\pm i\rangle = \frac{|0\rangle \pm i|1\rangle}{\sqrt{2}}$, which would be very similar to the case of $X$, i.e., $Y|\pm i\rangle = \pm|\pm i\rangle$.
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