B Peculiar View of Density Matrices: Is There a Problem?

[Heidi]

Hi Pfs , happy new year.
I wonder if there is a problem with the manner i see density matrices:
I use to consider them without a statistical point of view , just like i do with Hilbert vectors. no more no less. So the points on the Block sphere are only pecular points of those which are inside.
Of course if they can also describe mixtures of pure states in a statistical point of view.
is there a problem with that point of view?

 

[anuttarasammyak]

As for the titled question, I think yes because I have no idea for information to add to density matrix.

 

[ohwilleke]

Hi Pfs , happy new year.
I wonder if there is a problem with the manner i see density matrices:
I use to consider them without a statistical point of view , just like i do with Hilbert vectors. no more no less. So the points on the Block sphere are only pecular points of those which are inside.
Of course if they can also describe mixtures of pure states in a statistical point of view.
is there a problem with that point of view?

Could you give an example? Density matrices are used in more than one context, some of which might be more complete than others.

 

[vanhees71]

The quantum state of an arbitrary system is described by the statistical operator $\hat{\rho}$, which is a positive semidefinite self-adjoint operator with trace 1. It's a pure state, if it can be written as $\hat{\rho}=|\psi \rangle \langle \psi|$ with some normalized vector $|\psi \rangle$, i.e., iff $\hat{\rho}^2=\hat{\rho}$.