For someone who thinks that the state is associated with the observer (a subject) rather than the experiment (an object) there is no true state, only subjective assignments. But for a frequentist, the state contains true information about an ensemble of experiments. Or what else should distinguish the frequentist from the Bayesian?It always seemed to me if you were going to view the quantum state in a probabilistic way then pure states are states of maximal knowledge rather than the "true state".
Pure and mixed states are different ensembles, representing different statistics (if one could do experiments differentiating the two) and hence different objective realities. Only one of them is real.In a frequentist approach they'd be ensembles with minimal entropy. Either way they're not ignorance of the true pure state.
For a 2-state system (polarized beams of light) one can easily differentiate between light prepared in an unpolarized state (true density matrix = 1/2 unit matrix) and a completely polarized state (true density matrix of rank 1), and - in the limit of an unrestricted number of experiments - one can find out the true state by quantum tomography.
On the other hand, a consequent Bayesian who doesn't know how the light is prepared and thinks to be entitled by Jaynes or de Finetti to treat his complete lack of knowledge in terms of the natural noninformative prior will assign to both cases the same density matrix (1/2 unit matrix), and will lose millions of dollars in the second case should he bet that much on the resulting statistics.
Thus the correct state of a 2-state system, whether pure or mixed, conveys complete knowledge about the objective information that can possibly be obtained, while any significantly different state will lead to the wrong statistics. This must be part of any orthodoxy that can claim agreement with experiment.
I don't think that anything changes for bigger quantum systems simply because quantum tomography is no longer practically feasible. (The example of interference of quantum systems, which can be shown for larger and larger systems, suggests that there is no ''complexity border'' beyond which the principles change.)
You could instead go forward and solve the mathematical challenges involved in the thermal interpretation! There everything is as well-defined as in Constructive Field Theory but as the subject matter is new, it is not as hard to make significant progress!I'm going back to simpler topics like Constructive Field Theory!