# Worked Problems in Physics

## Nielsen and Chuang Exercise 2.61

Posted in Nielsen/Chuang by rpmuller on March 24, 2010

Exercise 2.61 Calculate the probability of obtaining the result ${+1}$ for a measurement of ${(\vec v\cdot\vec\sigma)}$, given that the state prior to measurement is ${\left|0\right>}$. What is the state of the system after the measurement if ${+1}$ is obtained?

The probability is given by ${\left<0|P_+|0\right>=\frac{1+v_z}{2}}$. The state after a measurement of ${+1}$ is ${P_+\left|0\right>=\frac{1}{2}((1+v_z)\left|0\right>+(v_x+iv_y)\left|1\right>}$.