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>}.