Generalized reduction criterion for separability of quantum states

A new necessary separability criterion that relates the structures of the total density matrix and its reductions is given. The method used is based on the realignment method [K. Chen and L.A. Wu, Quant. Inf. Comput. 3, 193 (2003)]. The new separability criterion naturally generalizes the reduction separability criterion introduced independently in previous work of [M. Horodecki and P. Horodecki, Phys. Rev. A 59, 4206 (1999)] and [N.J. Cerf, C. Adami and R.M. Gingrich, Phys. Rev. A 60, 898 (1999)]. In special cases, it recovers the previous reduction criterion and the recent generalized partial transposition criterion [K. Chen and L.A. Wu, Phys. Lett. A 306, 14 (2002)]. The criterion involves only simple matrix manipulations and can therefore be easily applied.Comment: 17 pages, 2 figure

Wigner Functions and Separability for Finite Systems

A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of dimension p^n where p is a prime number. With this limitation it is possible to define a phase space and Wigner functions in close analogy to the continuous case. That is, we use a phase space that is a direct sum of n two-dimensional vector spaces each containing p^2 points. This is in contrast to the more usual choice of a two-dimensional phase space containing p^(2n) points. A useful aspect of this approach is that we can relate complete separability of density matrices and their Wigner functions in a natural way. We discuss this in detail for bipartite systems and present the generalization to arbitrary numbers of subsystems when p is odd. Special attention is required for two qubits (p=2) and our technique fails to establish the separability property for more than two qubits.Comment: Some misprints have been corrected and a proof of the separability of the A matrices has been adde

Evolving faces from principal components

A system that uses an underlying genetic algorithm to evolve faces in response to user selection is described. The descriptions of faces used by the system are derived from a statistical analysis of a set of faces. The faces used for generation are transformed to an average shape by defining locations around each face and morphing. The shape-free images and shape vectors are then separately subjected to principal components analysis. Novel faces are generated by recombining the image components ("eigenfaces") and then morphing their shape according to the principal components of the shape vectors ("eigenshapes"). The prototype system indicates that such statistical analysis of a set of faces can produce plausible, randomly generated photographic images

Multicomplementary operators via finite Fourier transform

A complete set of d+1 mutually unbiased bases exists in a Hilbert spaces of dimension d, whenever d is a power of a prime. We discuss a simple construction of d+1 disjoint classes (each one having d-1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail.Comment: 15 pages, no figure

Quantum Measurement of a Single Spin using Magnetic Resonance Force Microscopy

Single-spin detection is one of the important challenges facing the development of several new technologies, e.g. single-spin transistors and solid-state quantum computation. Magnetic resonance force microscopy with a cyclic adiabatic inversion, which utilizes a cantilever oscillations driven by a single spin, is a promising technique to solve this problem. We have studied the quantum dynamics of a single spin interacting with a quasiclassical cantilever. It was found that in a similar fashion to the Stern-Gerlach interferometer the quantum dynamics generates a quantum superposition of two quasiclassical trajectories of the cantilever which are related to the two spin projections on the direction of the effective magnetic field in the rotating reference frame. Our results show that quantum jumps will not prevent a single-spin measurement if the coupling between the cantilever vibrations and the spin is small in comparison with the amplitude of the radio-frequency external field.Comment: 16 pages RevTeX including 4 figure

MicroRNAs Induced During Adipogenesis that Accelerate Fat Cell Development Are Downregulated in Obesity

OBJECTIVE-- We investigated the regulation and involvement of microRNAs (miRNAs) in fat cell development and obesity. RESEARCH DESIGN AND METHODS- Using miRNA microarrays, we profiled the expression of >370 miRNAs during adipogenesis of preadipocyte 3T3-L1 cells and adipocytes from leptin deficient ob/ob and diet-induced obese mice. Changes in key miRNAs were validated by RT-PCR. We further assessed the contribution of the chronic inflammatory environment in obese adipose tissue to the dysregulated miRNA expression by tumor necrosis factor (TNF)-α treatment of adipocytes. We functionally characterized two adipocyte-enriched miRNAs, miR-103 and miR-143, by a gain-of-function approach. RESULTS--Similar miRNAs were differentially regulated during in vitro and in vivo adipogenesis. Importantly, miRNAs that were induced during adipogenesis were downregulated in adipocytes from both types of obese mice and vice versa. These changes are likely associated with the chronic inflammatory environment, since they were mimicked by TNF-α treatment of differentiated adipocytes. Ectopic expression of miR-103 or miR-143 in preadipocytes accelerated adipogenesis, as measured both by the upregulation of many adipogenesis markers and by an increase in triglyceride accumulation at an early stage of adipogenesis. CONCLUSIONS- Our results provide the first experimental evidence for miR-103 function in adipose biology. The remarkable inverse regulatory pattern for many miRNAs during adipogenesis and obesity has important implications for understanding adipose tissue dysfunction in obese mice and humans and the link between chronic inflammation and obesity with insulin resistance

An overview of the first 5 years of the ENIGMA obsessive–compulsive disorder working group: The power of worldwide collaboration

Abstract Neuroimaging has played an important part in advancing our understanding of the neurobiology of obsessive?compulsive disorder (OCD). At the same time, neuroimaging studies of OCD have had notable limitations, including reliance on relatively small samples. International collaborative efforts to increase statistical power by combining samples from across sites have been bolstered by the ENIGMA consortium; this provides specific technical expertise for conducting multi-site analyses, as well as access to a collaborative community of neuroimaging scientists. In this article, we outline the background to, development of, and initial findings from ENIGMA's OCD working group, which currently consists of 47 samples from 34 institutes in 15 countries on 5 continents, with a total sample of 2,323 OCD patients and 2,325 healthy controls. Initial work has focused on studies of cortical thickness and subcortical volumes, structural connectivity, and brain lateralization in children, adolescents and adults with OCD, also including the study on the commonalities and distinctions across different neurodevelopment disorders. Additional work is ongoing, employing machine learning techniques. Findings to date have contributed to the development of neurobiological models of OCD, have provided an important model of global scientific collaboration, and have had a number of clinical implications. Importantly, our work has shed new light on questions about whether structural and functional alterations found in OCD reflect neurodevelopmental changes, effects of the disease process, or medication impacts. We conclude with a summary of ongoing work by ENIGMA-OCD, and a consideration of future directions for neuroimaging research on OCD within and beyond ENIGMA

Immuno-Golgi as a Tool for Analyzing Neuronal 3D-Dendritic Structure in Phenotypically Characterized Neurons

Characterization of neuronal dendritic structure in combination with the determination of specific neuronal phenotype or temporal generation is a challenging task. Here we present a novel method that combines bromodioxyuridine (BrdU) immunohistochemistry with Golgi-impregnation technique; with this simple non-invasive method, we are able to determine the tridimensional structure of dendritic arborization and spine shape of neurons born at a specific time in the hippocampus of adult animals. This analysis is relevant in physiological and pathological conditions in which altered neurogenesis is implicated, such as aging or emotional disorders