Bipartite quantum systems: on the realignment criterion and beyond

Inspired by the `computable cross norm' or `realignment' criterion, we propose a new point of view about the characterization of the states of bipartite quantum systems. We consider a Schmidt decomposition of a bipartite density operator. The corresponding Schmidt coefficients, or the associated symmetric polynomials, are regarded as quantities that can be used to characterize bipartite quantum states. In particular, starting from the realignment criterion, a family of necessary conditions for the separability of bipartite quantum states is derived. We conjecture that these conditions, which are weaker than the parent criterion, can be strengthened in such a way to obtain a new family of criteria that are independent of the original one. This conjecture is supported by numerical examples for the low dimensional cases. These ideas can be applied to the study of quantum channels, leading to a relation between the rate of contraction of a map and its ability to preserve entanglement.Comment: 19 pages, 4 figures, improved versio

Coarse grained and fine dynamics in trapped ion Raman schemes

A novel result concerning Raman coupling schemes in the context of trapped ions is obtained. By means of an operator perturbative approach, it is shown that the complete time evolution of these systems (in the interaction picture) can be expressed, with a high degree of accuracy, as the product of two unitary evolutions. The first one describes the time evolution related to an effective coarse grained dynamics. The second is a suitable correction restoring the {\em fine} dynamics suppressed by the coarse graining performed to adiabatically eliminate the nonresonantly coupled atomic level.Comment: 12 pages, no figure

Robustness against parametric noise of non ideal holonomic gates

Holonomic gates for quantum computation are commonly considered to be robust against certain kinds of parametric noise, the very motivation of this robustness being the geometric character of the transformation achieved in the adiabatic limit. On the other hand, the effects of decoherence are expected to become more and more relevant when the adiabatic limit is approached. Starting from the system described by Florio et al. [Phys. Rev. A 73, 022327 (2006)], here we discuss the behavior of non ideal holonomic gates at finite operational time, i.e., far before the adiabatic limit is reached. We have considered several models of parametric noise and studied the robustness of finite time gates. The obtained results suggest that the finite time gates present some effects of cancellation of the perturbations introduced by the noise which mimic the geometrical cancellation effect of standard holonomic gates. Nevertheless, a careful analysis of the results leads to the conclusion that these effects are related to a dynamical instead of geometrical feature.Comment: 8 pages, 8 figures, several changes made, accepted for publication on Phys. Rev.

Dynamical decoherence in a cavity with a large number of two-level atoms

We consider a large number of two-level atoms interacting with the mode of a cavity in the rotating-wave approximation (Tavis-Cummings model). We apply the Holstein-Primakoff transformation to study the model in the limit of the number of two-level atoms, all in their ground state, becoming very large. The unitary evolution that we obtain in this approximation is applied to a macroscopic superposition state showing that, when the coherent states forming the superposition are enough distant, then the state collapses on a single coherent state describing a classical radiation mode. This appear as a true dynamical effect that could be observed in experiments with cavities.Comment: 9 pages, no figures. This submission substitutes paper quant-ph/0212148 that was withdrawn. Version accepted for publication in Journal of Physics B: Atomic, Molecular & Optical Physic

Classical Tensors and Quantum Entanglement I: Pure States

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy

Quantum response of dephasing open systems

We develop a theory of adiabatic response for open systems governed by Lindblad evolutions. The theory determines the dependence of the response coefficients on the dephasing rates and allows for residual dissipation even when the ground state is protected by a spectral gap. We give quantum response a geometric interpretation in terms of Hilbert space projections: For a two level system and, more generally, for systems with suitable functional form of the dephasing, the dissipative and non-dissipative parts of the response are linked to a metric and to a symplectic form. The metric is the Fubini-Study metric and the symplectic form is the adiabatic curvature. When the metric and symplectic structures are compatible the non-dissipative part of the inverse matrix of response coefficients turns out to be immune to dephasing. We give three examples of physical systems whose quantum states induce compatible metric and symplectic structures on control space: The qubit, coherent states and a model of the integer quantum Hall effect.Comment: Article rewritten, two appendices added. 16 pages, 2 figure

A new perturbative expansion of the time evolution operator associated with a quantum system

A novel expansion of the evolution operator associated with a -- in general, time-dependent -- perturbed quantum Hamiltonian is presented. It is shown that it has a wide range of possible realizations that can be fitted according to computational convenience or to satisfy specific requirements. As a remarkable example, the quantum Hamiltonian describing a laser-driven trapped ion is studied in detail.Comment: 32 pages; modified version with examples of my previous paper quant-ph/0404056; to appear on the J. of Optics B: Quantum and Semiclassical Optics, Special Issue on 'Optics and Squeeze Transformations after Einstein

An Algebraic Approach to Linear-Optical Schemes for Deterministic Quantum Computing

Linear-Optical Passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the algebraic structure of LOP transformations and quantum computing. We first show how to decompose the Fock space of N optical modes in finite-dimensional subspaces that are suitable for encoding strings of qubits and invariant under LOP transformations (these subspaces are related to the spaces of irreducible unitary representations of U(N)). Next we show how to design in algorithmic fashion LOP circuits which implement any quantum circuit deterministically. We also present some simple examples, such as the circuits implementing a CNOT gate and a Bell-State Generator/Analyzer.Comment: new version with minor modification

Micrometeoroid Events in LISA Pathfinder

The zodiacal dust complex, a population of dust and small particles that pervades the Solar System, provides important insight into the formation and dynamics of planets, comets, asteroids, and other bodies. Here we present a new set of data obtained using a novel technique: direct measurements of momentum transfer to a spacecraft from individual particle impacts. This technique is made possible by the extreme precision of the instruments flown on the LISA Pathfinder spacecraft, a technology demonstrator for a future space-based gravitational wave observatory that operated near the first Sun-Earth Lagrange point from early 2016 through Summer of 2017. Using a simple model of the impacts and knowledge of the control system, we show that it is possible to detect impacts and measure properties such as the transferred momentum (related to the particle's mass and velocity), direction of travel, and location of impact on the spacecraft. In this paper, we present the results of a systematic search for impacts during 4348 hours of Pathfinder data. We report a total of 54 candidates with momenta ranging from 0.2$\,\mu\textrm{Ns}$ to 230$\,\mu\textrm{Ns}$. We furthermore make a comparison of these candidates with models of micrometeoroid populations in the inner solar system including those resulting from Jupiter-family comets, Oort-cloud comets, Hailey-type comets, and Asteroids. We find that our measured population is consistent with a population dominated by Jupiter-family comets with some evidence for a smaller contribution from Hailey-type comets. This is in agreement with consensus models of the zodiacal dust complex in the momentum range sampled by LISA Pathfinder.Comment: 22 pages, 14 figures, accepted in Ap

Educational intervention improves fruit and vegetable intake in young adults with metabolic syndrome components

The FRUVEDomics study investigates the effect of a diet intervention focused on increasing fruit and vegetable intake on the gut microbiome and cardiovascular health of young adults with/at risk for metabolic syndrome(MetS). It was hypothesized that the recommended diet would result in metabolic and gut microbiome changes. The 9-week dietary intervention adhered to the US Department of Agriculture Dietary Guidelines for Americansand focused on increasing fruit and vegetable intake to equal half of the diet. Seventeen eligible young adults with/or at high risk of MetS consented and completed preintervention and postintervention measurements, including anthropometric, body composition, cardiovascular, complete blood lipid panel, and collection of stool sample for microbial analysis. Participants attended weekly consultations to assess food logs, food receipts, and adherence to the diet. Following intention-to-treat guidelines, all 17 individuals were included in the dietary, clinical, and anthropometric analysis. Fruit and vegetable intake increased from 1.6 to 3.4 cups of fruits and vegetables (P \u3c .001) daily. Total fiber (P = .02) and insoluble fiber (P \u3c .0001) also increased. Clinical laboratory changes included an increase in sodium (P = .0006) and low-density lipoprotein cholesterol (P = .04). In the fecal microbiome, Erysipelotrichaceae (phylum Firmicutes) decreased (log2 fold change: −1.78, P = .01) and Caulobacteraceae (phylum Proteobacteria) increased (log2 fold change = 1.07, P = .01). Implementing a free-living 9-week diet, with intensive education and accountability, gave young adults at high risk for/or diagnosed with MetS the knowledge, skills, and feedback to improve diet. To yield greater impact, a longer diet intervention may be needed in this population