# What is the difference between complex and real coherneces?

If we have one density matrix

$$\rho=\begin{bmatrix}1/2&&1/2\\1/2&&1/2\end{bmatrix}$$

for the state $\lvert\psi\rangle=\frac{1}{\sqrt2}(\lvert g\rangle+\lvert e\rangle)$

and a different one

$$\rho=\begin{bmatrix}1/2&&i/2\\-i/2&&1/2\end{bmatrix}$$

for the state $\lvert\psi\rangle=\frac{1}{\sqrt2}(i\lvert g\rangle+\lvert e\rangle)$

What are the differences between these two states? Is there some physical meaning?

• Have you tried to compare the norms of these states? – Ice-Nine Feb 6 '18 at 13:10
• @Ice-Nine they are both 1 right? – James Feb 6 '18 at 13:41
• suggest you change title to "difference between complex and real coherences". "imaginary" could imply you're imagining things. – ZeroTheHero Feb 6 '18 at 13:47
• What is the effect of the complex rather than real phase difference? – ZeroTheHero Feb 6 '18 at 13:48