Retrodiction of Generalised Measurement Outcomes

If a generalised measurement is performed on a quantum system and we do not know the outcome, are we able to retrodict it with a second measurement? We obtain a necessary and sufficient condition for perfect retrodiction of the outcome of a known generalised measurement, given the final state, for an arbitrary initial state. From this, we deduce that, when the input and output Hilbert spaces have equal (finite) dimension, it is impossible to perfectly retrodict the outcome of any fine-grained measurement (where each POVM element corresponds to a single Kraus operator) for all initial states unless the measurement is unitarily equivalent to a projective measurement. It also enables us to show that every POVM can be realised in such a way that perfect outcome retrodiction is possible for an arbitrary initial state when the number of outcomes does not exceed the output Hilbert space dimension. We then consider the situation where the initial state is not arbitrary, though it may be entangled, and describe the conditions under which unambiguous outcome retrodiction is possible for a fine-grained generalised measurement. We find that this is possible for some state if the Kraus operators are linearly independent. This condition is also necessary when the Kraus operators are non-singular. From this, we deduce that every trace-preserving quantum operation is associated with a generalised measurement whose outcome is unambiguously retrodictable for some initial state, and also that a set of unitary operators can be unambiguously discriminated iff they are linearly independent. We then examine the issue of unambiguous outcome retrodiction without entanglement. This has important connections with the theory of locally linearly dependent and locally linearly independent operators.Comment: To appear in Physical Review

A framework for bounding nonlocality of state discrimination

We consider the class of protocols that can be implemented by local quantum operations and classical communication (LOCC) between two parties. In particular, we focus on the task of discriminating a known set of quantum states by LOCC. Building on the work in the paper "Quantum nonlocality without entanglement" [BDF+99], we provide a framework for bounding the amount of nonlocality in a given set of bipartite quantum states in terms of a lower bound on the probability of error in any LOCC discrimination protocol. We apply our framework to an orthonormal product basis known as the domino states and obtain an alternative and simplified proof that quantifies its nonlocality. We generalize this result for similar bases in larger dimensions, as well as the "rotated" domino states, resolving a long-standing open question [BDF+99].Comment: 33 pages, 7 figures, 1 tabl

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

Ethnohistory: a review of the method and its applicability to the study of rural Malaysia.

Ethnohistory is a methodological approach to the study of socio-cultural behavior which combines the strengths of ethnographic and historical research. The thesis of this paper is that such an approach offers an integrated perspective of social process not obtainable otherwise, therefore representing a valuable methodological tool to the anthropologist studying socio-cultural change. Malaysia, whose historical background of cultural change and culture contact is richly documented, offers great potential for ethnohistorical research. The first part of the paper briefly reviews the relation between history and anthropology during the last three-quarters of a century. Following that is a description of the aims of the ethnohistorical approach, and the data sources by which those aims are implemented. The paper concludes by illustrating the usefulness of the ethnohistorical method in a study of rural socio-cultural change, and appeals for greater interdisciplinary cooperation between historians and anthropologists

Herbivore-Driven Disruption of Arbuscular Mycorrhizal Carbon-for-Nutrient Exchange is Ameliorated by Neighbouring Plants

Arbuscular mycorrhizal fungi colonise the roots of most terrestrial plants, forming a globally significant symbiosis which is typically characterised by bi-directional exchange of fungal-acquired nutrients for plant fixed-carbon. Mycorrhizal fungi can form networks belowground with potential to facilitate the movement of carbon, nutrients, and defence signals across plant communities. The importance of neighbours in the mediation of carbon for nutrient exchange between mycorrhizal fungi and their plant hosts remains equivocal, particularly when other competing pressures for host plant resources are present. We manipulated the carbon source and sink strengths of neighbouring pairs of host plants through exposure to aphids and tracked the movement of carbon and nutrients with isotope tracers across the mycorrhizal fungal networks. When the carbon sink strengths of both neighbouring plants were increased by introduction of aphids, plant carbon supply to extraradical mycorrhizal fungal hyphae was reduced, but mycorrhizal phosphorus supply to both plants was maintained. However, when the sink strength of only one of the neighbouring plants was increased by aphid herbivory, carbon supply to the mycorrhizal fungal hyphae was restored. Our results show that the loss of carbon inputs into extraradical mycorrhizal fungal hyphae from one plant may be ameliorated through the inputs of a neighbouring plant, demonstrating the responsiveness and resilience of mycorrhizal plant communities to biological stressors. We show that mycorrhizal nutrient exchange dynamics are better understood as community-wide interactions between multiple players rather than being driven by strict exchanges between individual plants and their symbionts

Statistical modelling of annual variation for inference on stochastic population dynamics using Integral Projection Models

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