Characterization and quantification of symmetric Gaussian state entanglement through a local classicality criterion

A necessary and sufficient condition for characterization and quantification of entanglement of any bipartite Gaussian state belonging to a special symmetry class is given in terms of classicality measures of one-party states. For Gaussian states whose local covariance matrices have equal determinants it is shown that separability of a two-party state and classicality of one party state are completely equivalent to each other under a nonlocal operation, allowing entanglement features to be understood in terms of any available classicality measure.Comment: 5 pages, 1 figure. Replaced with final published versio

Strategy Logic with Imperfect Information

We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii, and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, the problem turns out to be undecidable. We introduce a syntactical class of "hierarchical instances" for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications are concerned with finer observations of the model. We prove that model-checking SLii restricted to hierarchical instances is decidable. This result, because it allows for complex patterns of existential and universal quantification on strategies, greatly generalises previous ones, such as decidability of multi-player games with imperfect information and hierarchical observations, and decidability of distributed synthesis for hierarchical systems. To establish the decidability result, we introduce and study QCTL*ii, an extension of QCTL* (itself an extension of CTL* with second-order quantification over atomic propositions) by parameterising its quantifiers with observations. The simple syntax of QCTL* ii allows us to provide a conceptually neat reduction of SLii to QCTL*ii that separates concerns, allowing one to forget about strategies and players and focus solely on second-order quantification. While the model-checking problem of QCTL*ii is, in general, undecidable, we identify a syntactic fragment of hierarchical formulas and prove, using an automata-theoretic approach, that it is decidable. The decidability result for SLii follows since the reduction maps hierarchical instances of SLii to hierarchical formulas of QCTL*ii

Interpretable Deep Learning applied to Plant Stress Phenotyping

Availability of an explainable deep learning model that can be applied to practical real world scenarios and in turn, can consistently, rapidly and accurately identify specific and minute traits in applicable fields of biological sciences, is scarce. Here we consider one such real world example viz., accurate identification, classification and quantification of biotic and abiotic stresses in crop research and production. Up until now, this has been predominantly done manually by visual inspection and require specialized training. However, such techniques are hindered by subjectivity resulting from inter- and intra-rater cognitive variability. Here, we demonstrate the ability of a machine learning framework to identify and classify a diverse set of foliar stresses in the soybean plant with remarkable accuracy. We also present an explanation mechanism using gradient-weighted class activation mapping that isolates the visual symptoms used by the model to make predictions. This unsupervised identification of unique visual symptoms for each stress provides a quantitative measure of stress severity, allowing for identification, classification and quantification in one framework. The learnt model appears to be agnostic to species and make good predictions for other (non-soybean) species, demonstrating an ability of transfer learning

Bipartite entanglement of quantum states in a pair basis

The unambiguous detection and quantification of entanglement is a hot topic of scientific research, though it is limited to low dimensions or specific classes of states. Here we identify an additional class of quantum states, for which bipartite entanglement measures can be efficiently computed, providing new rigorous results. Such states are written in arbitrary $d\times d$ dimensions, where each basis state in the subsystem A is paired with only one state in B. This new class, that we refer to as pair basis states, is remarkably relevant in many physical situations, including quantum optics. We find that negativity is a necessary and sufficient measure of entanglement for mixtures of states written in the same pair basis. We also provide analytical expressions for a tight lower-bound estimation of the entanglement of formation, a central quantity in quantum information.Comment: 8 pages, 10 figure