- #1
LagrangeEuler
- 717
- 20
Homework Statement
Find condition for which ##\hat{\rho}## will be pure state density operator?
##\hat{\rho} = \begin{bmatrix}
1+a_1 & a_2 \\[0.3em]
a_2^* & 1-a_1
\end{bmatrix}##
Homework Equations
In case of pure state ##Tr(\hat{\rho}^2)=Tr(\hat{\rho})=1##.
The Attempt at a Solution
Using that condition I got
##\hat{\rho}^2 = \begin{bmatrix}
(1+a_1)^2+|a_2|^2 & (1+a_1)a_2+a_2(1-a_1) \\[0.3em]
(1+a_1)a_2^*+a_2^*(1-a_1) & (1-a_1)^2+|a_2|^2
\end{bmatrix}##
and from that
## 2|a|^2+2a_1^2=-1## which can not be true. Because ##a_1## must be real, condition to ##\hat{\rho}## is hermitian.