Explore the Concept of Density Matrix with Jensa: A Comprehensive Guide

[barnflakes]

Thank you jensa.

 

[jensa]

Don't know where this expression comes from or why it is useful but it's quite simple to show that it is true. If the density matrix is normalized to unity then you should have $\rho_{11}+\rho_{22}=1$. Then in your equation you just substitute $1=(\rho_{11}+\rho_{22})^2$ so that you get $(\rho_{11}+\rho_{22})^2-(\rho_{11}-\rho_{22})^2=4\rho_{11}\rho_{22}$