The following article:

http://cmathphil.blogspot.com/2008/07/on-penroses-argument-against-density.html

addresses Penrose’s criticism (Penrose, 2004, The Road to Reality) of
the usage of the density operator when dealing with pure quantum
states. The main arguments of Penrose are reviewed, and the reflection
proceeds around the main question: What is the most fundamental
mathematical structure that should be used to describe the quantum
system, and, what is the nature of the physical semantics that this
structure formalizes?

The following reproduces the main text of the article, safe for the
formulas that appear as images (that can be seen in the above link):

On Penrose's Argument Against Density Operators
by Carlos Pedro Gonçalves

What is a quantum state?

Should we speak of a quantum state at all?

Should we speak of quantum states or of quantum processes?