Ruling out Higher-Order Interference from Purity Principles

As first noted by Rafael Sorkin, there is a limit to quantum interference. The interference pattern formed in a multi-slit experiment is a function of the interference patterns formed between pairs of slits; there are no genuinely new features resulting from considering three slits instead of two. Sorkin has introduced a hierarchy of mathematically conceivable higher-order interference behaviours, where classical theory lies at the first level of this hierarchy and quantum theory theory at the second. Informally, the order in this hierarchy corresponds to the number of slits on which the interference pattern has an irreducible dependence. Many authors have wondered why quantum interference is limited to the second level of this hierarchy. Does the existence of higher-order interference violate some natural physical principle that we believe should be fundamental? In the current work we show that such principles can be found which limit interference behaviour to second-order, or “quantum-like”, interference, but that do not restrict us to the entire quantum formalism. We work within the operational framework of generalised probabilistic theories, and prove that any theory satisfying Causality, Purity Preservation, Pure Sharpness, and Purification—four principles that formalise the fundamental character of purity in nature—exhibits at most second-order interference. Hence these theories are, at least conceptually, very “close” to quantum theory. Along the way we show that systems in such theories correspond to Euclidean Jordan algebras. Hence, they are self-dual and, moreover, multi-slit experiments in such theories are described by pure projectors

Deriving Grover's lower bound from simple physical principles

Grover's algorithm constitutes the optimal quantum solution to the search problem and provides a quadratic speed-up over all possible classical search algorithms. Quantum interference between computational paths has been posited as a key resource behind this computational speed-up. However there is a limit to this interference, at most pairs of paths can ever interact in a fundamental way. Could more interference imply more computational power? Sorkin has defined a hierarchy of possible interference behaviours—currently under experimental investigation—where classical theory is at the first level of the hierarchy and quantum theory belongs to the second. Informally, the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment. In this work, we consider how Grover's speed-up depends on the order of interference in a theory. Surprisingly, we show that the quadratic lower bound holds regardless of the order of interference. Thus, at least from the point of view of the search problem, post-quantum interference does not imply a computational speed-up over quantum theory

Generalised phase kick-back: the structure of computational algorithms from physical principles

The advent of quantum computing has challenged classical conceptions of which problems are efficiently solvable in our physical world. This motivates the general study of how physical principles bound computational power. In this paper we show that some of the essential machinery of quantum computation—namely reversible controlled transformations and the phase kick-back mechanism—exist in any operational-defined theory with a consistent notion of information. These results provide the tools for an exploration of the physics underpinning the structure of computational algorithms. We investigate the relationship between interference behaviour and computational power, demonstrating that non-trivial interference behaviour is a general resource for post-classical computation. In proving the above, we connect higher-order interference to the existence of post-quantum particle types, potentially providing a novel experimental test for higher-order interference. Finally, we conjecture that theories with post-quantum interference—the higher-order interference of Sorkin—can solve problems intractable even on a quantum computer

Higher-Order Interference in Extensions of Quantum Theory

Quantum interference, manifest in the two slit experiment, lies at the heart of several quantum computational speed-ups and provides a striking example of a quantum phenomenon with no classical counterpart. An intriguing feature of quantum interference arises in a variant of the standard two slit experiment, in which there are three, rather than two, slits. The interference pattern in this set-up can be written in terms of the two and one slit patterns obtained by blocking one, or more, of the slits. This is in stark contrast with the standard two slit experiment, where the interference pattern cannot be written as a sum of the one slit patterns. This was first noted by Rafael Sorkin, who raised the question of why quantum theory only exhibits irreducible interference in the two slit experiment. One approach to this problem is to compare the predictions of quantum theory to those of operationally-defined ‘foil’ theories, in the hope of determining whether theories that do exhibit higher-order interference suffer from pathological—or at least undesirable—features. In this paper two proposed extensions of quantum theory are considered: the theory of Density Cubes proposed by Dakić, Paterek and Brukner, which has been shown to exhibit irreducible interference in the three slit set-up, and the Quartic Quantum Theory of Życzkowski. The theory of Density Cubes will be shown to provide an advantage over quantum theory in a certain computational task and to posses a well-defined mechanism which leads to the emergence of quantum theory—analogous to the emergence of classical physics from quantum theory via decoherence. Despite this, the axioms used to define Density Cubes will be shown to be insufficient to uniquely characterise the theory. In comparison, Quartic Quantum Theory is a well-defined theory and we demonstrate that it exhibits irreducible interference to all orders. This feature of Życzkowski’s theory is argued not to be a genuine phenomenon, but to arise from an ambiguity in the current definition of higher-order interference in operationally-defined theories. Thus, to begin to understand why quantum theory is limited to a certain kind of interference, a new definition of higher-order interference is needed that is applicable to, and makes good operational sense in, arbitrary operationally-defined theories

A semantic web approach for built heritage representation

In a built heritage process, meant as a structured system of activities aimed at the investigation, preservation, and management of architectural heritage, any task accomplished by the several actors involved in it is deeply influenced by the way the knowledge is represented and shared. In the current heritage practice, knowledge representation and management have shown several limitations due to the difficulty of dealing with large amount of extremely heterogeneous data. On this basis, this research aims at extending semantic web approaches and technologies to architectural heritage knowledge management in order to provide an integrated and multidisciplinary representation of the artifact and of the knowledge necessary to support any decision or any intervention and management activity. To this purpose, an ontology-based system, representing the knowledge related to the artifact and its contexts, has been developed through the formalization of domain-specific entities and relationships between them

Better working memory and motor inhibition in children who delayed gratification

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EMI due to electric field coupling on PCB

In switching converter circuits, EM noise can couple between PCB traces through the effect of electric field coupling. An experiment using a flyback converter verifies the severity of this effect. Further experiments and field plots confirm that a good PCB layout can significantly reduce conducted EMI due to unintentional E-field coupling.published_or_final_versio

On defining the Hamiltonian beyond quantum theory

Energy is a crucial concept within classical and quantum physics. An essential tool to quantify energy is the Hamiltonian. Here, we consider how to define a Hamiltonian in general probabilistic theories, a framework in which quantum theory is a special case. We list desiderata which the definition should meet. For 3-dimensional systems, we provide a fully-defined recipe which satisfies these desiderata. We discuss the higher dimensional case where some freedom of choice is left remaining. We apply the definition to example toy theories, and discuss how the quantum notion of time evolution as a phase between energy eigenstates generalises to other theories.Comment: Authors' accepted manuscript for inclusion in the Foundations of Physics topical collection on Foundational Aspects of Quantum Informatio

Maternal antibodies from mothers of children with autism alter brain growth and social behavior development in the rhesus monkey.

Antibodies directed against fetal brain proteins of 37 and 73 kDa molecular weight are found in approximately 12% of mothers who have children with autism spectrum disorder (ASD), but not in mothers of typically developing children. This finding has raised the possibility that these immunoglobulin G (IgG) class antibodies cross the placenta during pregnancy and impact brain development, leading to one form of ASD. We evaluated the pathogenic potential of these antibodies by using a nonhuman primate model. IgG was isolated from mothers of children with ASD (IgG-ASD) and of typically developing children (IgG-CON). The purified IgG was administered to two groups of female rhesus monkeys (IgG-ASD; n=8 and IgG-CON; n=8) during the first and second trimesters of pregnancy. Another control group of pregnant monkeys (n=8) was untreated. Brain and behavioral development of the offspring were assessed for 2 years. Behavioral differences were first detected when the macaque mothers responded to their IgG-ASD offspring with heightened protectiveness during early development. As they matured, IgG-ASD offspring consistently deviated from species-typical social norms by more frequently approaching familiar peers. The increased approach was not reciprocated and did not lead to sustained social interactions. Even more striking, IgG-ASD offspring displayed inappropriate approach behavior to unfamiliar peers, clearly deviating from normal macaque social behavior. Longitudinal magnetic resonance imaging analyses revealed that male IgG-ASD offspring had enlarged brain volume compared with controls. White matter volume increases appeared to be driving the brain differences in the IgG-ASD offspring and these differences were most pronounced in the frontal lobes

The unfamiliar face effect on forensic craniofacial reconstruction and recognition.

Previous research into the reliability of forensic craniofacial reconstruction (CFR) has focused primarily on the accuracy of reconstructed faces from European or African ancestry skulls. Moreover, the recognition of CFR in relation to the experience and ancestry of the practitioners and the assessors has not been previously considered. The cross-race effect is a recognised phenomenon in psychology studies, where familiar ancestry faces are recognised more readily than unfamiliar ancestry faces, but there is a paucity of research addressing the relationship between the accuracy of reconstructed faces and the familiarity with this ancestry by the practitioners/assessors. The aims of this research were to investigate whether 'unfamiliar-race effect' has any influence on the accuracy of CFR and to evaluate how much the correct recognition rate of CFR is affected by the cross-race effect. Eight CFRs from three ancestry groups were produced by experienced practitioners in order to explore the aims. The results demonstrated that practitioners produced more recognisable CFRs using skulls from a familiar ancestry than skulls from unfamiliar ancestries