Ignorance Interpretation of Quantum Mechanics

However, the main question is still open. Does a given mixed state admit at all “ignorance interpretation”? In other words, is it allowed to assume that a system S with the mixed state WS = _ piP[ϕi] is actually in one of the pure states ϕi, which is, however, unknown to the observer who knows only the probabilities pi. If this interpretation of WS were correct, then the mixed state would express the observers “ignorance” of the actual pure state but not the objective indeterminacy of this state. It is one of the most fundamental results of quantum mechanics that a mixed state in general does not admit “ignorance interpretation”. The reason for this result is that the assumption of a objectively decided pure state leads in general to contradictions with well established results in quantum mechanics. This can be shown in various ways and on different levels of generality [4, 5]. See also States, pure and mixed, and their representations.