Negative Quasi-Probability as a Resource for Quantum Computation

A central problem in quantum information is to determine the minimal physical resources that are required for quantum computational speedup and, in particular, for fault-tolerant quantum computation. We establish a remarkable connection between the potential for quantum speed-up and the onset of negative values in a distinguished quasi-probability representation, a discrete analog of the Wigner function for quantum systems of odd dimension. This connection allows us to resolve an open question on the existence of bound states for magic-state distillation: we prove that there exist mixed states outside the convex hull of stabilizer states that cannot be distilled to non-stabilizer target states using stabilizer operations. We also provide an efficient simulation protocol for Clifford circuits that extends to a large class of mixed states, including bound universal states.Comment: 15 pages v4: This is a major revision. In particular, we have added a new section detailing an explicit extension of the Gottesman-Knill simulation protocol to deal with positively represented states and measurement (even when these are non-stabilizer). This paper also includes significant elaboration on the two main results of the previous versio

Association between overweight, obesity and self-perceived job insecurity in German employees

<p>Abstract</p> <p>Background</p> <p>Recent studies have shown an association between job insecurity and morbidity as well as mortality, however until now, knowledge about a potential association between job insecurity and overweight or obesity has been lacking.</p> <p>Methods</p> <p>In order to identify a possible association between job insecurity and overweight or obesity, we analysed data from the German Socioeconomic Panel (GSOEP) 2004/2005, a longitudinal study of private households in Germany. In this representative cohort of the German adult population, living and working conditions were observed. Data on Body Mass Index (BMI) and self-perceived probability of job loss within the next 2 years were available for 10,747 adults either employed or attending training programs.</p> <p>Results</p> <p>We identified 5,216 (49%) individuals as being overweight (BMI > 25 kg/m²) and 1,358(13%) individuals as being obese (BMI > 30 kg/m²). A total of 5,941 (55%) participants reported having concerns regarding job insecurity. In the multivariate analysis - after adjustment for relevant confounders - a statistically significant association between obesity and job insecurity (100% probability for losing the job in the following two years) could be observed with an adjusted odds ratio of 2.55 (95% confidence interval: 1.09-5.96).</p> <p>Conclusions</p> <p>Because of these results, we were able to conclude that overweight and obese persons perceive job insecurity more often than their normal weight counterparts in Germany and that the concurrence of obesity and job insecurity might lead employees into a vicious cycle. Further research with an emphasis on the occupational setting might be necessary in order to establish useful preventive programmes at the workplace.</p

A Quantum-Bayesian Route to Quantum-State Space

In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent's personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the usual probability rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper, we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum Bayesianism. The starting point is the representation of quantum states induced by a symmetric informationally complete measurement or SIC. In this representation, the Born rule takes the form of a particularly simple modification of the law of total probability. We show how to derive key features of quantum-state space from (i) the requirement that the Born rule arises as a simple modification of the law of total probability and (ii) a limited number of additional assumptions of a strong Bayesian flavor.Comment: 7 pages, 1 figure, to appear in Foundations of Physics; this is a condensation of the argument in arXiv:0906.2187v1 [quant-ph], with special attention paid to making all assumptions explici

Quantum Fourier transform, Heisenberg groups and quasiprobability distributions

This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a semiclassical approach to quantum probability distribution. This leads to studying certain functionals of a pair of "conjugate" observables, connected via the quantum Fourier transform. The Heisenberg groups emerge naturally from this study and we take a rapid look at their representations. The quantum Fourier transform appears as the intertwining operator of two equivalent representation arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of Wigner function from the marginal distributions via inverse Radon transform giving explicit formulas. We consider applications of our approach to quantum information processing and quantum process tomography.Comment: 39 page

Quasi-probability representations of quantum theory with applications to quantum information science

This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasi-probability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness.Comment: v3: typos fixed, references adde

Framed Hilbert space: hanging the quasi-probability pictures of quantum theory

Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an alternate approach to defining a set of quasi-probability representations, based on a more natural generalization of a classical representation, is equivalent to our earlier approach based on frames, and therefore is also subject to our no-go theorem for a non-negative representation. Furthermore, we clarify the relationship between the contextuality of quantum theory and the necessity of negativity in quasi-probability representations and discuss their relevance as criteria for non-classicality. We also provide a comprehensive overview of known quasi-probability representations and their expression within the frame formalism.Comment: 46 pages, 1 table, contains a review of finite dimensional quasi-probability function

Body-mass index and risk of obesity-related complex multimorbidity : an observational multicohort study

Background The accumulation of disparate diseases in complex multimorbidity makes prevention difficult if each disease is targeted separately. We aimed to examine obesity as a shared risk factor for common diseases, determine associations between obesity-related diseases, and examine the role of obesity in the development of complex multimorbidity (four or more comorbid diseases). Methods We did an observational study and used pooled prospective data from two Finnish cohort studies (the Health and Social Support Study and the Finnish Public Sector Study) comprising 114 657 adults aged 16-78 years at study entry (1998-2013). A cohort of 499 357 adults (aged 38-73 years at study entry; 2006-10) from the UK Biobank provided replication in an independent population. BMI and clinical characteristics were assessed at baseline. BMIs were categorised as obesity (Peer reviewe

Identification of the factors associated with outcomes in a condition management programme

&lt;p&gt;Background: A requirement of the Government’s Pathways to Work (PtW) agenda was to introduce a Condition Management Programme (CMP). The aim of the present study was to identify the differences between those who engaged and made progress in this telephone-based biopsychosocial intervention, in terms of their health, and those who did not and to determine the client and practitioner characteristics and programme elements associated with success in a programme aimed at improving health.&lt;/p&gt; &lt;p&gt;Methods: Data were obtained from the CMP electronic spreadsheets and clients paper-based case records. CMP standard practice was that questionnaires were administered during the pre- and post-assessment phases over the telephone. Each client’s record contains their socio-demographic data, their primary health condition, as well as the pre- and post-intervention scores of the health assessment tool administered. Univariate and multivariate statistical analysis was used to investigate the relationships between the database variables. Clients were included in the study if their records were available for analysis from July 2006 to December 2007.&lt;/p&gt; &lt;p&gt; Results: On average there were 112 referrals per month, totalling 2016 referrals during the evaluation period. The majority (62.8%) of clients had a mental-health condition. Successful completion of the programme was 28.5% (575 “completers”; 144 “discharges”). Several factors, such as age, health condition, mode of contact, and practitioner characteristics, were significant determinants of participation and completion of the programme. The results showed that completion of the CMP was associated with a better mental-health status, by reducing the number of clients that were either anxious, depressed or both, before undertaking the programme, from 74% to 32.5%.&lt;/p&gt; &lt;p&gt;Conclusions: Our findings showed that an individual's characteristics are associated with success in the programme, defined as completing the intervention and demonstrating an improved health status. This study provides some evidence that the systematic evaluation of such programmes and interventions could identify ways in which they could be improved.&lt;/p&gt

The Alignment Between 3-D Data and Articulated Shapes with Bending Surfaces

International audienceIn this paper we address the problem of aligning 3-D data with articulated shapes. This problem resides at the core of many motion tracking methods with applications in human motion capture, action recognition, medical-image analysis, etc. We describe an articulated and bending surface representation well suited for this task as well as a method which aligns (or registers) such a surface to 3-D data. Articulated objects, e.g., humans and animals, are covered with clothes and skin which may be seen as textured surfaces. These surfaces are both articulated and deformable and one realistic way to model them is to assume that they bend in the neighborhood of the shape's joints. We will introduce a surface-bending model as a function of the articulated-motion parameters. This combined articulated-motion and surface-bending model better predicts the observed phenomena in the data and therefore is well suited for surface registration. Given a set of sparse 3-D data (gathered with a stereo camera pair) and a textured, articulated, and bending surface, we describe a register-and-fit method that proceeds as follows. First, the data-to-surface registration problem is formalized as a classifier and is carried out using an EM algorithm. Second, the data-to-surface fitting problem is carried out by minimizing the distance from the registered data points to the surface over the joint variables. In order to illustrate the method we applied it to the problem of hand tracking. A hand model with 27 degrees of freedom is successfully registered and fitted to a sequence of 3-D data points gathered with a stereo camera pair

Body-mass index and risk of obesity-related complex multimorbidity: an observational multicohort study

BACKGROUND: The accumulation of disparate diseases in complex multimorbidity makes prevention difficult if each disease is targeted separately. We aimed to examine obesity as a shared risk factor for common diseases, determine associations between obesity-related diseases, and examine the role of obesity in the development of complex multimorbidity (four or more comorbid diseases). METHODS: We did an observational study and used pooled prospective data from two Finnish cohort studies (the Health and Social Support Study and the Finnish Public Sector Study) comprising 114 657 adults aged 16-78 years at study entry (1998-2013). A cohort of 499 357 adults (aged 38-73 years at study entry; 2006-10) from the UK Biobank provided replication in an independent population. BMI and clinical characteristics were assessed at baseline. BMIs were categorised as obesity (≥30·0 kg/m2), overweight (25·0-29·9 kg/m2), healthy weight (18·5-24·9 kg/m2), and underweight (<18·5 kg/m2). Via linkage to national health records, participants were followed-up for death and diseases diagnosed according to the International Classification of Diseases 10th Revision (ICD-10). Hazard ratios (HRs) with 95% CIs and population attributable fractions (PAFs) for associations between BMI and multimorbidity were calculated. FINDINGS: Mean follow-up duration was 12·1 years (SD 3·8) in the Finnish cohorts and 11·8 years (1·7) in the UK Biobank cohort. Obesity was associated with 21 non-overlapping cardiometabolic, digestive, respiratory, neurological, musculoskeletal, and infectious diseases after Bonferroni multiple testing adjustment and ignoring HRs of less than 1·50. Compared with healthy weight, the confounder-adjusted HR for obesity was 2·83 (95% CI 2·74-2·93; PAF 19·9% [95% CI 19·3-20·5]) for developing at least one obesity-related disease, 5·17 (4·84-5·53; 34·4% [33·2-35·5]) for two diseases, and 12·39 (9·26-16·58; 55·2% [50·9-57·5]) for complex multimorbidity. The proportion of participants of healthy weight with complex multimorbidity by age 75 years was observed by age 55 years in participants with obesity, and degree of obesity was associated with complex multimorbidity in a dose-response relationship. Compared with obesity, the association between overweight and complex multimorbidity was more modest (HR 2·67, 95% CI 1·94-3·68; PAF 13·3% [95% CI 9·6-16·3]). The same pattern of results was observed in the UK Biobank cohort. INTERPRETATION: Obesity is associated with diverse, increasing disease burdens, and might represent an important target for multimorbidity prevention that avoids the complexities of multitarget preventive regimens. FUNDING: Wellcome Trust, Medical Research Council, National Institute on Aging