# Worked Problems in Physics

## Nielsen and Chuang Exercise 2.74

Posted in Nielsen/Chuang by rpmuller on June 1, 2010

Exercise 2.74 Suppose a composite of systems ${A}$ and ${B}$ is in the state ${\left|a\right>\left|b\right>}$, where ${\left|a\right>}$ is a pure state of system ${A}$, and ${\left|b\right>}$ is a pure state of system ${B}$. Show that the reduced density operator of system ${A}$ alone is a pure state.

$\displaystyle \rho = \left|a\right>\left|b\right>\left

$\displaystyle \mathrm{tr}_B(\rho) = \left|a\right>\left= \left|a\right>\left

and is thus a pure state.