Scott: how does that let you decompose any density matrix uniquely into pure states?
Yes, that was a very bad thing I said. Because even if my density matrix is diagonal in one basis, if I nontrivially change basis it will no longer be diagonal, and so won’t be interpretable as a straightforward probability distribution over the new basis states. I must retract, retreat, and retrace my steps.
Scott: how does that let you decompose any density matrix uniquely into pure states?
Yes, that was a very bad thing I said. Because even if my density matrix is diagonal in one basis, if I nontrivially change basis it will no longer be diagonal, and so won’t be interpretable as a straightforward probability distribution over the new basis states. I must retract, retreat, and retrace my steps.