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Quantum electronics is significantly involved in the development of the fieldof quantum information processing. In this domain, the growth of Blind QuantumSource Separation and Blind Quantum Process Tomography has led, within theformalism of the Hilbert space, to the introduction of the concept of aRandom-Coefficient Pure State, or RCPS: the coefficients of its development inthe chosen basis are random variables. This paper first describes anexperimental situation necessitating its introduction. While the von Neumannapproach to a statistical mixture considers statistical properties of anobservable, in the presence of an RCPS one has to manipulate statisticalproperties of probabilities of measurement outcomes, these probabilities thenbeing themselves random variables. It is recalled that, in the presence of avon Neumann statistical mixture, the consistency of the density operator \r{ho}formalism is based on a postulate. The interest of the RCPS concept ispresented in the simple case of a spin 1/2, through two instances. The mostfrequent use of the \r{ho} formalism by users of quantum mechanics is amotivation for establishing some links between a given RCPS and the language ofthe density operator formalism, while keeping in mind that the situationdescribed by an RCPS is different from the one which has led to theintroduction of \r{ho}. It is established that the Landau - Feynman use of\r{ho} is mobilized in a situation differing from both the von Neumannstatistical mixture and the RCPS. It is shown that the use of the higher-ordermoments of a well-chosen random variable helps solving a problem alreadyidentified by Zeh in 1970.

Random-coefficient pure states, the density operator formalism and the Zeh problem