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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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