The notions of ideal, first kind, and repeatable measurements are reformulated and their relations analyzed within a systematic theory of measurement in quantum mechanics. This allows one to investigate new information theoretical characterizations of such measurements.
The theory of measurements continuous in time in quantum mechanics (quantum continual measurements) has been formulated by using the notions of instrument, positive operator valued measure, etc., by using quantum stochastic differential equations and by using classical stochastic differential equations (SDE's) for vectors in Hilbert spaces or for trace-class operators. In the same times Ozawa made developments in the theory of instruments and introduced the related notions of a posteriori states and of information gain [1]. In this paper we introduce a simple class of SDE's relevant to the theory of continual measurements and we recall how they are related to instruments and a posteriori states and, so, to the general formulation of quantum mechanics. Then we introduce and use the notion of information gain and the other results of the paper [1] inside the theory of continual measurements. [1] M. Ozawa, On information gain by quantum measurements of continuous observables, J. Math. Phys. 27 (1986) 759-763.
Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify uncertainty (and joint uncertainty). In this paper we use operational information-theoretic principles to identify the common essence of all such measures, thereby defining measure-independent notions of uncertainty and joint uncertainty. We find that most existing entropic uncertainty relations use measures of joint uncertainty that yield themselves to a small class of operational interpretations. Our notion relaxes this restriction, revealing previously unexplored joint uncertainty measures. To illustrate the utility of our formalism, we derive an uncertainty relation based on one such new measure. We also use our formalism to gain insight into the conditions under which measure-independent uncertainty relations can be found.
Quantum mechanics is often regarded as paradoxical or incomplete due to the imposition of a classical ontology that is not suited to its domain. This paper proposes a reinterpretation based on the notion of contextual coherence, in which the quantum state is not an intrinsic property but a relational configuration dependent on interaction conditions. Measurement is thus understood as a regime transition characterized by phase fixation and the dispersion of coherence into the environment. Within this framework, the Résonon is introduced as a minimal conceptual unit articulating energy, information, and temporal phase. It does not constitute a new physical entity but serves as a theoretical tool to express the internal logic of coherence transitions. This approach allows for a reformulation of superposition, contextuality, and decoherence without invoking additional assumptions such as many worlds or hidden variables. Finally, the paper opens an epistemological dialogue with operative knowledge systems such as Ifá, highlighting a convergence around the notion of preparing reality. Quantum mechanics thus emerges as a theory of coherence regimes in transition, where reality stabilizes through contextual configurations rather than as a set of pre-existing objects.