# Pure states and mixtures

1. Nov 14, 2013

### naima

Is there a way to write p1 |v1> + p2 |v2> if it is not a pure state but a mixture?
thanks.

2. Nov 14, 2013

### Jazzdude

If it is a true classical ensemble then no. However, if it's something that you got from tracing over unobserved degrees of freedom then yes. The representation is then the original pure state on the larger space.

Cheers,

Jazz

3. Nov 14, 2013

### naima

How to write correctly such a mixture?

4. Nov 14, 2013

### Jazzdude

Mixtures are hermitian operators or matrices. You can construct them from state vectors by taking a convex sum of their outer products. So for example

$\rho = a^* a \left|\psi\rangle \langle\psi\right| + b^* b \left|\phi\rangle \langle\phi\right|$

5. Nov 14, 2013

### naima

Ok
thank you
I did not realize that i could write it in this way.