Coherence

Given a Density Operator $\hat{\rho }$ and a basis $\{|i⟩\}$, we can write $\hat{\rho }={\sum }_{ij}{\rho }_{ij}|i⟩⟨j|$. In this situation we have:

• ${\rho }_{ij}$ is a coherence for $i\ne j$.
• ${\rho }_{ii}$ is a population, describing the probability of observing the value $|i⟩$.

In the image below, the population lies on the diagonal and all coherences are zero.