# Density operator of unknown system

1. Apr 20, 2013

### sunrah

1. The problem statement, all variables and given/known data
What is the density operator (statistical operator) of a system about which nothing is known?

2. Relevant equations

$\hat{\rho} = \sum p_{i} |i\rangle\langle i|$

3. The attempt at a solution

If nothing is known about a system we must assume something in order to make worthwhile statements about it. So if no one state can be preferred over another then it seems a normal distribution of states is likely. This means for N states the $p_{i} = \frac{1}{N}$

Putting this in the general definition of density operator gives

$\hat{\rho} = \frac{1}{N} \sum |i\rangle\langle i| = \frac{1}{N}\cdot \hat{1}$

Really?

2. Apr 21, 2013

### dextercioby

Looks good to me.