Minus-i state $\lvert -i\rangle$ (also written $\lvert -y\rangle$) is a quantum state that is an equal superposition of $\lvert 0\rangle$ and $\lvert 1\rangle$ with a relative phase of $-i$. It is one of the six cardinal states on the Bloch sphere, sitting at the negative $y$-axis with coordinates $(0, -1, 0)$.

$$\lvert -i\rangle = \frac{1}{\sqrt{2}}\lvert 0\rangle - \frac{i}{\sqrt{2}}\lvert 1\rangle = \frac{1}{\sqrt{2}}\begin{pmatrix}1\\-i\end{pmatrix}$$

It is an eigenstate of the Pauli-Y gate with eigenvalue $-1$, meaning $Y\lvert -i\rangle = -\lvert -i\rangle$. When measured in the computational basis, it collapses to $\lvert 0\rangle$ or $\lvert 1\rangle$ each with probability $1/2$. Together with $\lvert i\rangle$, it forms the $Y$ eigenbasis $\{\lvert i\rangle, \lvert -i\rangle\}$.