Symmetry, Compact Closure and Dagger Compactness for Categories of Convex Operational Models

In the categorical approach to the foundations of quantum theory, one begins with a symmetric monoidal category, the objects of which represent physical systems, and the morphisms of which represent physical processes. Usually, this category is taken to be at least compact closed, and more often, dagger compact, enforcing a certain self-duality, whereby preparation processes (roughly, states) are interconvertible with processes of registration (roughly, measurement outcomes). This is in contrast to the more concrete “operational” approach, in which the states and measurement outcomes associated with a physical system are represented in terms of what we here call a convex operational model: a certain dual pair of ordered linear spaces–generally, not isomorphic to one another. On the other hand, state spaces for which there is such an isomorphism, which we term weakly self-dual, play an important role in reconstructions of various quantum-information theoretic protocols, including teleportation and ensemble steering. In this paper, we characterize compact closure of symmetric monoidal categories of convex operational models in two ways: as a statement about the existence of teleportation protocols, and as the principle that every process allowed by that theory can be realized as an instance of a remote evaluation protocol—hence, as a form of classical probabilistic conditioning. In a large class of cases, which includes both the classical and quantum cases, the relevant compact closed categories are degenerate, in the weak sense that every object is its own dual. We characterize the dagger-compactness of such a category (with respect to the natural adjoint) in terms of the existence, for each system, of a symmetric bipartite state, the associated conditioning map of which is an isomorphism.     

Stimulus correlates of tachistoscopic discrimination-recognition performance: Compactness,jaggedness, and areal asymmetry

The utility of three physical dimensions (compactness, jaggedness, and areal asymmetry) of four-sided random forms on discrimination-recognition performance was examined. Six experimental conditions were defined by constructing discrimination-recognition problems wherein forms were paired on the basis of a high or low value on each of the three physical dimensions. Twenty-six Ss were randomly assigned to each experimental condition and were tested on five problems, four times at each of five single form duration times. Each problem presentation consisted of selecting which of two forms had been previously exposed at the selected duration. Analyses of the number of correct responses indicated support for the existence of a selective attention process and the utility of the compactness physical dimension.     

Advertisement for the ontology for medicine

The ontology of medicine—the question of whether disease entities are real or not—is an underdeveloped area of philosophical inquiry. This essay explains the primary question at issue in medical ontology, discusses why answering this question is important from both a philosophical and a practical perspective, and argues that the problem of medical ontology is unique, i.e., distinct, from the ontological problems raised by other sciences and therefore requires its own analysis.     

Evaluation of evidence for sufficiency, for necessity, and for necessity-and-sufficiency

We report two experiments with 120 undergraduate subjects. The tasks presented clearly articulated hypotheses concerning necessity, sufficiency, and necessity-and-sufficiency, together with possible combinations of treatment conditions, and required subjects to judge whether, according to the hypotheses, the relevant outcomes will occur, will not occur, or might occur. The patterns of responses reveal how subjects understand the extensions of the concepts, i.e. what each hypothesis permits, requires, and excludes. Only necessity-and-sufficiency hypotheses generally led to logically adequate responses, and the most typical error for both necessity hypotheses and sufficiency hypotheses was to treat them as extensionally equivalent to necessity-and-sufficiency. This error tendency was more evident for necessity than for sufficiency hypotheses. Further, although responses to both necessity hypotheses and sufficiency hypotheses were affected by the complexity of the hypothesized conditions, responses to necessity-and-sufficiency hypotheses were not. We argue that the results are not a function of a response bias but reflect differences in the way the hypotheses are understood. Implications for the causal attribution literature are discussed.