The Characterization of Noncontextuality in the Framework of Generalized Probabilistic Theories

To make precise the sense in which the operational predictions of quantum theory conflict with a classical worldview, it is necessary to articulate a notion of classicality within an operational framework. A widely applicable notion of classicality of this sort is whether or not the predictions of a given operational theory can be explained by a generalized-noncontextual ontological model. We here explore what notion of classicality this implies for the generalized probabilistic theory (GPT) that arises from a given operational theory, focusing on prepare-measure scenarios. We first show that, when mapping an operational theory to a GPT by quotienting relative to operational equivalences, the constraint of explainability by a generalized-noncontextual ontological model is mapped to the constraint of explainability by an ontological model. We then show that, under the additional assumption that the ontic state space is of finite cardinality, this constraint on the GPT can be expressed as a geometric condition which we term simplex-embeddability. Whereas the traditional notion of classicality for a GPT is that its state space be a simplex and its effect space be the dual of this simplex, simplex-embeddability merely requires that its state space be embeddable in a simplex and its effect space in the dual of that simplex. We argue that simplex-embeddability constitutes an intuitive and freestanding notion of classicality for GPTs. Our result also has applications to witnessing nonclassicality in prepare-measure experiments.Comment: 5 pages + 5 page appendi

Draft Genome Sequence of Escherichia coli K-12 (ATCC 29425)

A draft genome sequence for Escherichia coli ATCC 29425 was investigated. The size of the genome was 4,608,319 bp, with an observed G+C content of 50.68%. This assembly consisted of 80 contigs, with an average coverage of 122.2×, including one contig representative of the complete genome for the temperate phage P1

Quantifying Bell: the Resource Theory of Nonclassicality of Common-Cause Boxes

We take a resource-theoretic approach to the problem of quantifying nonclassicality in Bell scenarios. The resources are conceptualized as probabilistic processes from the setting variables to the outcome variables having a particular causal structure, namely, one wherein the wings are only connected by a common cause. We term them "common-cause boxes". We define the distinction between classical and nonclassical resources in terms of whether or not a classical causal model can explain the correlations. One can then quantify the relative nonclassicality of resources by considering their interconvertibility relative to the set of operations that can be implemented using a classical common cause (which correspond to local operations and shared randomness). We prove that the set of free operations forms a polytope, which in turn allows us to derive an efficient algorithm for deciding whether one resource can be converted to another. We moreover define two distinct monotones with simple closed-form expressions in the two-party binary-setting binary-outcome scenario, and use these to reveal various properties of the pre-order of resources, including a lower bound on the cardinality of any complete set of monotones. In particular, we show that the information contained in the degrees of violation of facet-defining Bell inequalities is not sufficient for quantifying nonclassicality, even though it is sufficient for witnessing nonclassicality. Finally, we show that the continuous set of convexly extremal quantumly realizable correlations are all at the top of the pre-order of quantumly realizable correlations. In addition to providing new insights on Bell nonclassicality, our work also sets the stage for quantifying nonclassicality in more general causal networks.Comment: V4 changes: Accepted by Quantum, bibliography hyperlinks adjusted according to journal policy. Slight reorganization of content in Section

Draft Genome Sequence of Escherichia coli K-12 (ATCC 10798)

Here, we present the draft genome sequence of Escherichia coli ATCC 10798. E. coli ATCC 10798 is a K-12 strain, one of the most well-studied model microorganisms. The size of the genome was 4,685,496 bp, with a G+C content of 50.70%. This assembly consists of 62 contigs and the F plasmid

Draft Genome Sequence of Micrococcus luteus (Schroeter) Cohn (ATCC 12698)

The actinobacterium Micrococcus luteus can be found in a wide variety of habitats. Here, we report the 2,411,958-bp draft genome sequence of the type strain M. leuteus (Schroeter) Cohn (ATCC 12698). Characteristic of this taxa, the genome sequence has a high G+C content, 73.14%

Draft Genome Sequence of Enterococcus faecalis ATCC BAA-2128

While a part of the native gut microflora, the Gram-positive bacterium Enterococcus faecalis can lead to serious infections elsewhere in the body. The draft genome of E. faecalis strain ATCC BAA-2128, isolated from piglet feces, was examined. This draft genome consists of 42 contigs, 12 of which exhibit homology to annotated plasmids

Contextuality without incompatibility

The existence of incompatible measurements is often believed to be a feature of quantum theory which signals its inconsistency with any classical worldview. To prove the failure of classicality in the sense of Kochen-Specker noncontextuality, one does indeed require sets of incompatible measurements. However, a more broadly applicable and more permissive notion of classicality is the existence of a generalized-noncontextual ontological model. In particular, this notion can imply constraints on the representation of outcomes even within a single nonprojective measurement. We leverage this fact to demonstrate that measurement incompatibility is neither necessary nor sufficient for proofs of the failure of generalized noncontextuality. Furthermore, we show that every proof of the failure of generalized noncontextuality in a prepare-measure scenario can be converted into a proof of the failure of generalized noncontextuality in a corresponding scenario with no incompatible measurements