Geometric Entanglement of Symmetric States and the Majorana Representation

Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally entangled symmetric states of up to twelve qubits were explored, and their amount of geometric entanglement determined by numeric and analytic means. For this the Majorana representation, a generalization of the Bloch sphere representation, can be employed to represent symmetric n qubit states by n points on the surface of a unit sphere. Symmetries of this point distribution simplify the determination of the entanglement, and enable the study of quantum states in novel ways. Here it is shown that the duality relationship of Platonic solids has a counterpart in the Majorana representation, and that in general maximally entangled symmetric states neither correspond to anticoherent spin states nor to spherical designs. The usability of symmetric states as resources for measurement-based quantum computing is also discussed.Comment: 10 pages, 8 figures; submitted to Lecture Notes in Computer Science (LNCS

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease

Prevalence of Salmonella in grade A whole shell eggs in the island of Ireland

Following the emergence of Salmonella Enteritidis as a widespread contaminant of eggs and the role of eggs in the transmission of human salmonellosis, control measures were introduced to curb the spread of infection. Two approaches to Salmonella control are currently used by egg producers in Ireland, because Northern Ireland producers, like those in the rest of the United Kingdom, widely adopted a vaccination regime, whereas the Republic of Ireland does not permit vaccination but introduced controls based on routine monitoring for specific Salmonella serovars and subsequent culling of infected flocks. To compare the efficacy of these two approaches and determine the prevalence of salmonellae in eggs produced for retail sale in the island of Ireland, a major survey of approximately 30,000 grade A eggs was undertaken. Egg shells and contents were analyzed separately for salmonellae by procedures based on International Organization for Standardization methodology. The survey yielded only two positive samples, with Salmonella Infantis and Salmonella Montevideo isolated from shells; no egg contents yielded salmonellae. There was no statistically significant difference in the prevalence of salmonellae between eggs produced in Northern Ireland and those from the Republic of Ireland; hence, both regimes appeared to be equally effective in controlling salmonellae. The prevalence was also significantly lower than that found in a recent major United Kingdom survey. Hence, shell eggs produced in the island of Ireland are unlikely to be a source of human salmonellosi