We present a way to apply quantum logic to the study of quantum programs. This is made possible by using an extension of the usual propositional language in order to make transformations performed on the system appear explicitly. This way, the evolution of the system becomes part of the logical study. We show how both unitary operations and two-valued measurements can be included in this formalism and can thus be handled logically.

AimThe second Diabetes, Attitudes, Wishes and Needs (DAWN2™) multinational cross-sectional study was aimed at generating insights to facilitate innovative efforts by people with diabetes (PWD), family members (FMs), and health care professionals (HCPs) to improve self-management and psychosocial support in diabetes. Here, the French data from the DAWN2™ study are described.MethodsIn France, 500 PWD (80 with type 1 diabetes [T1] and 420 with type 2 diabetes [T2]), 120 FMs, and 288 HCPs were recruited. The questionnaires assessed the impact of diabetes on quality of life and mood, self-management, attitudes/beliefs, and care/support.ResultsDiabetes negatively impacted the emotional well-being of 59% of people with T1 versus 45% of people with T2 (P<0.05) and about half of FMs. A high level of distress was felt by about half of PWD and FMs. About half of HCPs reported assessing depression in their patients. Sixty-two percent of FMs considered managing diabetes to be a burden. Hypoglycemia was a source of concern for 64% of people with T1 and 73% of FMs of insulin users. About two-thirds of non-insulin-medicated people with T2 agreed to start insulin if prescribed, while half of HCPs preferred to delay insulin initiation. A discrepancy between HCPs’ perceptions of their interactions with their patients and PWD’s recollection of these interactions with regard to patients’ personal needs and distress was also observed.ConclusionWhile distress remains under-assessed by HCPs, the negative impact of diabetes on the lives of PWD and FMs clearly induces distress on both groups. These findings provide new understanding of barriers precluding optimal management of diabetes. Developing strategies to overcome these barriers is now warranted.

We introduce and formalize a notion of "a priori knowledge" about a quantum system, and show some properties about this form of knowledge. Finally, we show that the Kochen-Specker theorem follows directly from this study.

One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the question whether such a representation is complete has been debated since almost the early days of quantum mechanics. In this article, we develop an alternate way to formalize knowledge about the state of quantum systems, based solely on experimentally accessible elements, namely on outcomes of finite measurements. We introduce what we call partial description which, given a feasible measurement, indicates some outcomes which are known to be impossible (i.e. known to have a probability equal to 0 to occur) and hence have to be discarded. Then, we introduce partial states (which are partial descriptions providing as much information as possible) and compare this way to describe quantum states to the orthodox one, using vector rays. Finally, we show that partial states allow to describe quantum states in a strictly more expressive way that the orthodox description does

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In this article, we present what we believe to be a simple way to motivate the use of Hilbert spaces in quantum mechanics. To achieve this, we study the way the notion of dimension can, at a very primitive level, be defined as the cardinality of a maximal collection of mutually orthogonal elements (which, for instance, can be seen as spatial directions). Following this idea, we develop a formalism based on two basic ingredients, namely an orthogonality relation and matroids which are a very generic algebraic structure permitting to define a notion of dimension. Having obtained what we call orthomatroids, we then show that, in high enough dimension, the basic constituants of orthomatroids (more precisely the simple and irreducible ones) are isomorphic to generalized Hilbert lattices, so that their presence is a direct consequence of an orthogonality-based characterization of dimension.

Two important classes of quantum structures, namely orthomodular posets and orthomodular lattices, can be characterized in a classical context, using notions like partial information and points of view. Using the formalism of representation systems, we show that these quantum structures can be obtained by expressing conditions on the existence of particular points of view, of particular ways to observe a system.