All Mutually Unbiased Product Bases in Dimension Six

All mutually unbiased bases in dimension six consisting of product states only are constructed. Several continuous families of pairs and two triples of mutually unbiased product bases are found to exist but no quadruple. The exhaustive classification leads to a proof that a complete set of seven mutually unbiased bases, if it exists, cannot contain a triple of mutually unbiased product bases.Comment: 32 pages, 3 figures, identical to published versio

S’auto évaluer pour agir : rôle du sentiment d’efficacité personnelle dans les pratiques d’enseignement

Dans son quotidien, l’enseignant est amené à prendre des décisions, évaluer les éléments favorables du contexte, mobiliser des ressources afin d’organiser l’activité pédagogique. L’ensemble de ces choix tactiques ou stratégiques est sous-tendu par un processus d’auto-évaluation de son action que nous avons souhaité analyser. Au sein du collège les enseignants vivent en direct la nécessaire adaptation de leur projet pédagogique à la spécificité des élèves et à la différenciation de leurs actes. Ces enseignants, entre deux rives, ont au quotidien à la fois, à conduire leur activité, à auto évaluer celle-ci et à construire des pratiques efficaces. Notre recherche nous permet de décrire et d’expliquer le rôle des processus internes d’auto-évaluation des actions professionnelles. Ces procédures sont en interaction avec la construction chez l’enseignant d’un sentiment d’auto-efficacité qui, au-delà de renforcer l’estime de soi, est un véritable moteur de la valorisation et de la production des actes d’enseignement.<br>In their day to day work, teachers are required to make decisions, evaluate the positive elements in their environment and mobilize resources in order to organize their pedagogical activity. All of these tactical or strategic choices are underlain by a self-evaluation process of their action that we have chosen to analyze. In junior high school, teachers get to see how it is necessary to adapt their pedagogical projects to students’ specificity and to differentiated acts. Daily, these teachers have, at the same time, to conduct their activity, to self-evaluate it and to conceive efficient practices. This study enables us to better describe and explain the role of internal self-assessment processes of professional actions. These self-evaluation processes interact with the building of a sense of efficiency that, beyond strengthening teachers’ self-esteem, is a true engine of development and production of acts of education

Linking Entanglement Detection and State Tomography via Quantum 2-Designs

We present an experimentally feasible and efficient method for detecting entangled states with measurements that extend naturally to a tomographically complete set. Our detection criterion is based on measurements from subsets of a quantum 2-design, e.g., mutually unbiased bases or symmetric informationally complete states, and has several advantages over standard entanglement witnesses. First, as more detectors in the measurement are applied, there is a higher chance of witnessing a larger set of entangled states, in such a way that the measurement setting converges to a complete setup for quantum state tomography. Secondly, our method is twice as effective as standard witnesses in the sense that both upper and lower bounds can be derived. Thirdly, the scheme can be readily applied to measurement-device-independent scenarios.Comment: 16 pages, 4 figure

On the Impossibility to Extend Triples of Mutually Unbiased Product Bases in Dimension Six

An analytic proof is given which shows that it is impossible to extend any triple of mutually unbiased (MU) product bases in dimension six by a single MU vector. Furthermore, the 16 states obtained by removing two orthogonal states from any MU product triple cannot figure in a (hypothetical) complete set of seven MU bases. These results follow from exploiting the structure of MU product bases in a novel fashion, and they are among the strongest ones obtained for MU bases in dimension six without recourse to computer algebra.Comment: 12 pages, identical to published versio

Amount of quantum coherence needed for measurement incompatibility

A pair of quantum observables diagonal in the same "incoherent" basis can be measured jointly, so some coherence is obviously required for measurement incompatibility. Here we first observe that coherence in a single observable is linked to the diagonal elements of any observable jointly measurable with it, leading to a general criterion for the coherence needed for incompatibility. Specialising to the case where the second observable is incoherent (diagonal), we develop a concrete method for solving incompatibility problems, tractable even in large systems by analytical bounds, without resorting to numerical optimisation. We verify the consistency of our method by a quick proof of the known noise bound for mutually unbiased bases, and apply it to study emergent classicality in the spin-boson model of an N-qubit open quantum system. Finally, we formulate our theory in an operational resource-theoretic setting involving "genuinely incoherent operations" used previously in the literature, and show that if the coherence is insufficient to sustain incompatibility, the associated joint measurements have sequential implementations via incoherent instruments.Comment: 19 pages, 3 figures, identical to published versio

The wider value of rural rail provision

In the context of recent plans for public sector expenditure, the value for money provided by rural public transport is an important issue in Britain and elsewhere, and one aspect of this is the option and non-use value placed on public transport by residents. Whilst there are a small number of studies which have estimated option and non-use values, they rest largely on contingent valuation methods which are subject to dangers of bias, and concentrate on commuter services into cities rather than truly rural services. This paper seeks to overcome these problems by conducting a Stated Preference (SP) experiment in rural communities, which values the provision of rail services and compares this against Post Office provision. We believe that using this approach, and allowing respondents to compare willingness to pay for rail services with that for another important rural service subject to threatened cuts, should produce more reliable results; moreover we achieve this using self completion questionnaires rather than much more expensive interviews. Our results show much lower values for rail than previous studies, though this is to be expected in truly rural areas where the likelihood of commuting by rail is much lower. Other non-use values are greater than option values in this context

Food neophobia across the life course: Pooling data from five national cross-sectional surveys in Ireland

Food neophobia describes a reluctance to eat novel foods. Levels of food neophobia vary throughout life and are thought to peak in childhood. However, the trajectory of food neophobia across the life course is not fully clear. Using data from five national cross-sectional surveys in Ireland we explored levels of food neophobia in males and females aged 1–87 years. In addition, we assessed the influence of sociodemographic factors, breastfeeding and parental food neophobia on food neophobia. Food neophobia was measured using the Food Neophobia Scale in adults and adolescents and with the Children\u27s Eating Behaviour Questionnaire in preschool and school aged children. A total of 3246 participants (female, 49.9%) were included. Food neophobia increased with age from 1 to ∼6 years, then decreased until early adulthood where it remained stable until increasing with age in older adults (\u3e54 years). In adults, lower education level, social class and rural residency were associated with higher food neophobia. When preschool and school aged children surveys were pooled (ages 1–12), higher food neophobia was seen in males, children with lower parental education and those who were not breastfed. Sociodemographic factors were not significantly associated with food neophobia in adolescents. Breastfeeding duration was negatively associated with food neophobia in children and adolescents and parental food neophobia was positively associated with child\u27s food neophobia in preschool and school aged children. The influence of socioeconomic factors was more pronounced in adults than in children or adolescents. However, sociodemographic factors only explained a small proportion of the variation in food neophobia across all ages. Longitudinal studies are needed to understand how changes in age or socioeconomic circumstance influence food neophobia at an individual level