Higher-order interference in extensions of quantum theory

Quantum interference lies at the heart of several quantum computational speed-ups and provides a striking example of a phenomenon with no classical counterpart. An intriguing feature of quantum interference arises in a three slit experiment. In this set-up, the interference pattern can be written in terms of the two and one slit patterns obtained by blocking some of the slits. This is in stark contrast with the standard two slit experiment, where the interference pattern is irreducible. This was first noted by Rafael Sorkin, who asked 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 exhibiting 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 Dakic et al., which has been shown to exhibit irreducible interference in the three slit set-up, and the Quartic Quantum Theory of Zyczkowski. 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. 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 well-defined and we show that it exhibits irreducible interference to all orders. This feature of the theory is argued not to be a genuine phenomenon, but to arise from an ambiguity in the current definition of higher-order interference. To understand why quantum theory has limited interference therefore, a new operational definition of higher-order interference is needed.Comment: Updated in response to referee comments. 17 pages. Comments welcom

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.Comment: Updated title and exposition in response to referee comments. 6+2 pages, 5 figure

A digital control system for high level acoustic noise generation

As part of the modernization of the Acoustic Test Facility at Lockheed Missiles and Space Company, Sunnyvale, a digital acoustic control system was designed and built. The requirements imposed by Lockheed on the control system and the degree to which those requirements were met are discussed. Acceptance test results as well as some of the features of the digital control system not found in traditional manual control systems are discussed

Oracles and query lower bounds in generalised probabilistic theories

We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying three natural physical principles possess a well-defined oracle model. Indeed, we prove a subroutine theorem for oracles in such theories which is a necessary condition for the oracle to be well-defined. The three principles are: causality (roughly, no signalling from the future), purification (each mixed state arises as the marginal of a pure state of a larger system), and strong symmetry existence of non-trivial reversible transformations). Sorkin has defined a hierarchy of conceivable interference behaviours, where the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment. Given our oracle model, we show that if a classical computer requires at least n queries to solve a learning problem, then the corresponding lower bound in theories lying at the kth level of Sorkin's hierarchy is n/k. Hence, lower bounds on the number of queries to a quantum oracle needed to solve certain problems are not optimal in the space of all generalised probabilistic theories, although it is not yet known whether the optimal bounds are achievable in general. Hence searches for higher-order interference are not only foundationally motivated, but constitute a search for a computational resource beyond that offered by quantum computation.Comment: 17+7 pages. Comments Welcome. Published in special issue "Foundational Aspects of Quantum Information" in Foundations of Physic

Telecommunications and economic growth: an empirical analysis of sub-saharan Africa

We examine the effect on economic growth of mobile cellular phones in sub-Saharan Africa where a marked asymmetry is present between land-line penetration and mobile telecommunications expansion. This study extends previous ones along two important dimensions. First, we allow for the potential endogeneity between economic growth and telecommunications expansion by employing a special linear generalized method of moments (GMM) estimator. Second, we explicitly model for varying degrees of substitutability between mobile cellular and land-line telephony, so that greater expansion of mobile telecommunications can have a different impact whenever the level of land-line penetration differs. We find that mobile cellular phone expansion is an important determinant of the rate of economic growth in Sub-Saharan Africa. Moreover, we find that the contribution of mobile cellular phones to economic growth has been growing in importance in the region, and that the marginal impact of mobile telecommunication services is even greater wherever land-line phones are rare. Given the low cost of mobile telecommunications technology relative to other broad infrastructure projects, especially land-line infrastructure, we advocate that mobile telecommunication services be encouraged in the area.

Microgravity combustion of dust suspensions

Unlike the combustion of homogeneous gas mixtures, there are practically no reliable fundamental data (i.e., laminar burning velocity, flammability limits, quenching distance, minimum ignition energy) for the combustion of heterogeneous dust suspensions. Even the equilibrium thermodynamic data such as the constant pressure volume combustion pressure and the constant pressure adiabatic flame temperature are not accurately known for dust mixtures. This is mainly due to the problem of gravity sedimentation. In normal gravity, turbulence, convective flow, electric and acoustic fields are required to maintain a dust in suspension. These external influences have a dominating effect on the combustion processes. Microgravity offers a unique environment where a quiescent dust cloud can in principle be maintained for a sufficiently long duration for almost all combustion experiments (dust suspensions are inherently unstable due to Brownian motion and particle aggregation). Thus, the microgravity duration provided by drop towers, parabolic flights, and the space shuttle, can all be exploited for different kinds of dust combustion experiments. The present paper describes some recent studies on microgravity combustion of dust suspension carried out on the KC-135 and the Caravelle aircraft. The results reported are obtained from three parabolic flight campaigns

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.Comment: 18+8 pages. Comments welcome. v2: Minor correction to Lemma 5.1, main results are unchange

Eccomi pronto : implementation of a Socio-Emotional Development curriculum in a South Korean elementary school

‘Eccomi Pronto’ (EP), an elementary school socio-emotional learning curriculum that was originally developed and evaluated in Italy was translated in Korean and implemented and evaluated in 4th grade classrooms of a primary school in South Korea. Qualitative data from teachers indicated that EP improved the self-reflection and selfdirection of students, resulted in pedagogically useful insights into the psychological functioning of students, and enhanced the quality of teacher-student interaction. However, statistically significant changes in students’ engaged, academic behavior (as measured by an 8-item survey) were not noted. Teachers reported that the core of the EP curriculum was appropriate for the South Korean educational context. Teachers also recommended modifications in the follow-up learning activities to make these activities more consistent with South Korean education practices.peer-reviewe