Negative off-diagonal elements in density matrix?

[zje]

I have a quick question. I've been trying to search for an answer, but I'm probably looking in the wrong places.

Is it valid to have negative off-diagonal elements in a density matrix?

Thanks!

 

[Physics Monkey]

Sure, just take the density matrix for the state (up - down).

 

[tom.stoer]

Of course.

In diagonal form you can interpret the diagonal elements as probabilities. But in addition you know that all symmetric matrices can be diagonalized via a unitary transformation.