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

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

A no-go theorem for theories that decohere to quantum mechanics

To date, there has been no experimental evidence that invalidates quantum theory. Yet it may only be an effective description of the world, in the same way that classical physics is an effective description of the quantum world. We ask whether there exists an operationally defined theory superseding quantum theory, but which reduces to it via a decoherence-like mechanism. We prove that no such post-quantum theory exists if it is demanded that it satisfy two natural physical principles: causality and purification. Causality formalizes the statement that information propagates from present to future, and purification that each state of incomplete information arises in an essentially unique way due to lack of information about an environment. Hence, our result can be viewed either as evidence that the fundamental theory of Nature is quantum or as showing in a rigorous manner that any post-quantum theory must abandon causality, purification or both

Vacuum phototriodes for the CMS electromagnetic calorimeter endcap

The measurement of scintillation light from the lead tungstate crystals of the Compact Muon Solenoid (CMS) electromagnetic calorimeter (ECAL) poses a substantial technical challenge, particularly in the endcap regions, where the radiation levels are highest. The photodetectors must be fast, sensitive, radiationhard, and operate with significant internal gain in a magnetic field of 4 Tesla. The measured performance characteristics of the first batches of series production vacuum phototriodes (VPT), developed to satisfy the needs of CMS, will be described

SREBP1c-CRY1 signalling represses hepatic glucose production by promoting FOXO1 degradation during refeeding

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Students benefit from developing their own emergency medicine OSCE stations: a comparative study using the matched-pair method

Background: Students can improve the learning process by developing their own multiple choice questions. If a similar effect occurred when creating OSCE (objective structured clinical examination) stations by themselves it could be beneficial to involve them in the development of OSCE stations. This study investigates the effect of students developing emergency medicine OSCE stations on their test performance. Method: In the 2011/12 winter semester, an emergency medicine OSCE was held for the first time at the Faculty of Medicine at the University of Leipzig. When preparing for the OSCE, 13 students (the intervention group) developed and tested emergency medicine examination stations as a learning experience. Their subsequent OSCE performance was compared to that of 13 other students (the control group), who were parallelized in terms of age, gender, semester and level of previous knowledge using the matched-pair method. In addition, both groups were compared to 20 students who tested the OSCE prior to regular emergency medicine training (test OSCE group). Results: There were no differences between the three groups regarding age (24.3 +/- 2.6; 24.2 +/- 3.4 and 24 +/- 2.3 years) or previous knowledge (29.3 +/- 3.4; 29.3 +/- 3.2 and 28.9 +/- 4.7 points in the multiple choice {[} MC] exam in emergency medicine). Merely the gender distribution differed (8 female and 5 male students in the intervention and control group vs. 3 males and 17 females in the test OSCE group). In the exam OSCE, participants in the intervention group scored 233.4 +/- 6.3 points (mean +/- SD) compared to 223.8 +/- 9.2 points (p < 0.01) in the control group. Cohen's effect size was d = 1.24. The students of the test OSCE group scored 223.2 +/- 13.4 points. Conclusions: Students who actively develop OSCE stations when preparing for an emergency medicine OSCE achieve better exam results

Minimal Intervention Needed for Change: Definition, Use, and Value for Improving Health and Health Research

Much research focuses on producing maximal intervention effects. This has generally not resulted in interventions being rapidly or widely adopted or seen as feasible given resources, time, and expertise constraints in the majority of real-world settings. We present a definition and key characteristics of a minimum intervention needed to produce change (MINC). To illustrate use of a MINC condition, we describe a computer-assisted, interactive minimal intervention, titled Healthy Habits, used in three different controlled studies and its effects. This minimal intervention produced modest to sizable health behavior and psychosocial improvements, depending on the intensity of personal contacts, producing larger effects at longer-term assessments. MINC comparison conditions could help to advance both health care and health research, especially comparative effectiveness research. Policy and funding implications of requiring an intervention to be demonstrated more effective than a simpler, less costly MINC alternative are discussedYe

Evaluation of serum CEA, CYFRA21-1 and CA125 for the early detection of colorectal cancer using longitudinal preclinical samples

Blood-borne biomarkers for early detection of colorectal cancer (CRC) could markedly increase screening uptake. The aim of this study was to evaluate serum carcinoembryonic antigen (CEA), CYFRA21-1 and CA125 for the early detection of CRC in an asymptomatic cohort