TeX source:

\mathbf{E}_1\triangleq\dfrac{\sqrt{2}}{1+\sqrt{2}}|1\rangle\langle1|, \quad \mathbf{E}_2\triangleq\dfrac{\sqrt{2}}{2(1+\sqrt{2})}(|0\rangle-|1\rangle)(\langle0|-\langle1|), \qquad \mathbf{E}_3\triangleq\mathbf{I}-\mathbf{E}_1-\mathbf{E}_2.