Strong Complementarity and Non-locality in Categorical Quantum Mechanics

Categorical quantum mechanics studies quantum theory in the framework of dagger-compact closed categories. Using this framework, we establish a tight relationship between two key quantum theoretical notions: non-locality and complementarity. In particular, we establish a direct connection between Mermin-type non-locality scenarios, which we generalise to an arbitrary number of parties, using systems of arbitrary dimension, and performing arbitrary measurements, and a new stronger notion of complementarity which we introduce here. Our derivation of the fact that strong complementarity is a necessary condition for a Mermin scenario provides a crisp operational interpretation for strong complementarity. We also provide a complete classification of strongly complementary observables for quantum theory, something which has not yet been achieved for ordinary complementarity. Since our main results are expressed in the (diagrammatic) language of dagger-compact categories, they can be applied outside of quantum theory, in any setting which supports the purely algebraic notion of strongly complementary observables. We have therefore introduced a method for discussing non-locality in a wide variety of models in addition to quantum theory. The diagrammatic calculus substantially simplifies (and sometimes even trivialises) many of the derivations, and provides new insights. In particular, the diagrammatic computation of correlations clearly shows how local measurements interact to yield a global overall effect. In other words, we depict non-locality.Comment: 15 pages (incl. 5 appendix). To appear: LiCS 201

Macular hypoplasia in congenital disorder of glycosylation type 1a

Congenital disorders of glycosylation are a rare group of metabolic disorders that can result in multiorgan disease. This article describes a novel finding of macular hypoplasia in congenital disorders of glycosylation type 1a

Analysis of Lake Stratification and Mixing and Its Influencing Factors over High Elevation Large and Small Lakes on the Tibetan Plateau

Lake stratification and mixing processes can influence gas and energy transport in the water column and water–atmosphere interactions, thus impacting limnology and local climate. Featuring the largest high-elevation inland lake zone in the world, comprehensive and comparative studies on the evolution of lake stratification and mixing and their driving forces are still quite limited. Here, using valuable temperature chain measurements in four large lakes (Nam Co, Dagze Co, Bangong Co, and Paiku Co) and a “small lake” adjacent to Nam Co, our objectives are to investigate the seasonal and diurnal variations of epilimnion depth (Ep, the most important layer in stratification and mixing process) and to analyze the driving force differences between “small lake” and Nam Co. Results indicate that Ep estimated by the methods of the absolute density difference (&lt;0.1 kg m−3) from the surface and the Lake-Analyzer were quite similar, with the former being more reliable and widely applicable. The stratification and mixing in the four large lakes showed a dimictic pattern, with obvious spring and autumn turnovers. Additionally, the stratification form during heat storage periods, with Ep quickly locating at depths of approximately 10–15 m, and, after that, increasing gradually to the lake bottom. Additionally, the diurnal variation in Ep can be evidenced both in the large and small lakes when temperature measurements above 3 m depth are included. For Nam Co, the dominant influencing factors for the seasonal variation of Ep were the heat budget components (turbulent heat fluxes and radiation components), while wind speed only had a relatively weak positive correlation (r = 0.23). In the “small lake”, radiation components and wind speed show high negative (r = −0.43 to −0.59) and positive (r = 0.46) correlation, with rare correlations for turbulent heat flux. These reported characteristics have significance for lake process modeling and evaluation in these high-elevation lakes.</p