Efficient and feasible state tomography of quantum many-body systems

We present a novel method to perform quantum state tomography for many-particle systems which are particularly suitable for estimating states in lattice systems such as of ultra-cold atoms in optical lattices. We show that the need for measuring a tomographically complete set of observables can be overcome by letting the state evolve under some suitably chosen random circuits followed by the measurement of a single observable. We generalize known results about the approximation of unitary 2-designs, i.e., certain classes of random unitary matrices, by random quantum circuits and connect our findings to the theory of quantum compressed sensing. We show that for ultra-cold atoms in optical lattices established techniques like optical super-lattices, laser speckles, and time-of-flight measurements are sufficient to perform fully certified, assumption-free tomography. Combining our approach with tensor network methods - in particular the theory of matrix-product states - we identify situations where the effort of reconstruction is even constant in the number of lattice sites, allowing in principle to perform tomography on large-scale systems readily available in present experiments.Comment: 10 pages, 3 figures, minor corrections, discussion added, emphasizing that no single-site addressing is needed at any stage of the scheme when implemented in optical lattice system

Differential rotation and meridional flow in the solar supergranulation layer: Measuring the eddy viscosity

We measure the eddy viscosity in the outermost layers of the solar convection zone by comparing the rotation law computed with the Reynolds stress resulting from f-plane simulations of the angular momentum transport in rotating convection with the observed differential rotation pattern. The simulations lead to a negative vertical and a positive horizontal angular momentum transport. The consequence is a subrotation of the outermost layers, as it is indeed indicated both by helioseismology and the observed rotation rates of sunspots. In order to reproduce the observed gradient of the rotation rate a value of about 1.5 x 10^{13} cm/s for the eddy viscosity is necessary. Comparison with the magnetic eddy diffusivity derived from the sunspot decay yields a surprisingly large magnetic Prandtl number of 150 for the supergranulation layer. The negative gradient of the rotation rate also drives a surface meridional flow towards the poles, in agreement with the results from Doppler measurements. The successful reproduction of the abnormally positive horizontal cross correlation (on the northern hemisphere) observed for bipolar groups then provides an independent test for the resulting eddy viscosity.Comment: 6 pages, 8 figures, Astronomy and Astrophysics (subm.

Index theory of one dimensional quantum walks and cellular automata

If a one-dimensional quantum lattice system is subject to one step of a reversible discrete-time dynamics, it is intuitive that as much "quantum information" as moves into any given block of cells from the left, has to exit that block to the right. For two types of such systems - namely quantum walks and cellular automata - we make this intuition precise by defining an index, a quantity that measures the "net flow of quantum information" through the system. The index supplies a complete characterization of two properties of the discrete dynamics. First, two systems S_1, S_2 can be pieced together, in the sense that there is a system S which locally acts like S_1 in one region and like S_2 in some other region, if and only if S_1 and S_2 have the same index. Second, the index labels connected components of such systems: equality of the index is necessary and sufficient for the existence of a continuous deformation of S_1 into S_2. In the case of quantum walks, the index is integer-valued, whereas for cellular automata, it takes values in the group of positive rationals. In both cases, the map S -> ind S is a group homomorphism if composition of the discrete dynamics is taken as the group law of the quantum systems. Systems with trivial index are precisely those which can be realized by partitioned unitaries, and the prototypes of systems with non-trivial index are shifts.Comment: 38 pages. v2: added examples, terminology clarifie

Fate of CMY-2-encoding plasmids introduced into the human fecal microbiota by exogenous Escherichia coli

The gut is a hot spot for transfer of antibiotic resistance genes from ingested exogenous bacteria to the indigenous microbiota. The objective of this study was to determine the fate of two nearly identical blaCMY-2-harboring plasmids introduced into the human fecal microbiota by two Escherichia coli strains isolated from human and poultry meat, respectively. The chromosome and the CMY-2-encoding plasmid of both strains were labeled with distinct fluorescent markers (mCherry and GFP), allowing Fluorescence Activated Cell Sorting (FACS)-based tracking of the strain and the resident bacteria that have acquired its plasmid. Each strain was introduced into an established in vitro gut model (CoMiniGut) inoculated with individual feces from ten healthy volunteers. Fecal samples collected 2, 6 and 24 h after strain inoculation were analyzed by FACS and plate counts. Although the human strain survived better than the poultry meat strain, both strains transferred their plasmids to the fecal microbiota at concentrations as low as 102 CFU/mL. Strain survival and plasmid transfer varied significantly depending on inoculum concentration and individual fecal microbiota. Identification of transconjugants by 16S rRNA gene sequencing and MALDI-TOF mass spectrometry revealed that the plasmids were predominantly acquired by Enterobacteriaceae such as E. coli and Hafnia alvei. Our experimental data demonstrate that exogenous E. coli of human or animal origin can readily transfer CMY-2-encoding IncI1 plasmids to the human fecal microbiota. Low amounts of exogenous strain are sufficient to ensure plasmid transfer if the strain is able to survive the gastric environment

Hemispheric Sunspot Numbers R_n and R_s: Catalogue and N-S asymmetry analysis

Sunspot drawings are provided on a regular basis at the Kanzelhoehe Solar Observatory, Austria, and the derived relative sunspot numbers are reported to the Sunspot Index Data Center in Brussels. From the daily sunspot drawings, we derived the northern, R_n, and southern, R_s, relative sunspot numbers for the time span 1975-2000. In order to accord with the International Sunspot Numbers R_i, the R_n and R_s have been normalized to the R_i, which ensures that the relation R_n + R_s = R_i is fulfilled. For validation, the derived R_n and R_s are compared to the international northern and southern relative sunspot numbers, which are available from 1992. The regression analysis performed for the period 1992-2000 reveals good agreement with the International hemispheric Sunspot Numbers. The monthly mean and the smoothed monthly mean hemispheric Sunspot Numbers are compiled into a catalogue. Based on the derived hemispheric Sunspot Numbers, we study the significance of N-S asymmetries and the rotational behavior separately for both hemispheres. We obtain that about 60% of the monthly N-S asymmetries are significant at a 95% level, whereas the relative contributions of the northern and southern hemisphere are different for different cycles. From the analysis of power spectra and autocorrelation functions, we derive a rigid rotation with about 27 days for the northern hemisphere, which can be followed for up to 15 periods. Contrary to that, the southern hemisphere reveals a dominant period of about 28 days, whereas the autocorrelation is strongly attenuated after 3 periods. These findings suggest that the activity of the northern hemisphere is dominated by an active zone, whereas the southern activity is mainly dominated by individual long-lived sunspot groups.Comment: 9 pages, 8 figures, data catalogue online available at http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/390/70

Radiative emission of solar features in the Ca II K line: comparison of measurements and models

We study the radiative emission of various types of solar features, such as quiet Sun, enhanced network, plage, and bright plage regions, identified on filtergrams taken in the Ca II K line. We analysed fulldisk images obtained with the PSPT, by using three interference filters that sample the Ca II K line with different bandpasses. We studied the dependence of the radiative emission of disk features on the filter bandpass. We also performed a NLTE spectral synthesis of the Ca II K line integrated over the bandpass of PSPT filters. The synthesis was carried out by utilizing both the PRD and CRD with the most recent set of semi empirical atmosphere models in the literature and some earlier atmosphere models. We measured the CLV of intensity values for various solar features identified on PSPT images and compared the results obtained with those derived from the synthesis. We find that CRD calculations derived using the most recent quiet Sun model, on average, reproduce the measured values of the quiet Sun regions slightly more accurately than PRD computations with the same model. This may reflect that the utilized atmospheric model was computed assuming CRD. Calculations with PRD on earlier quiet Sun model atmospheres reproduce measured quantities with a similar accuracy as to that achieved here by applying CRD to the recent model. We also find that the median contrast values measured for most of the identified bright features, disk positions, and filter widths are, on average, a factor 1.9 lower than those derived from PRD simulations performed using the recent bright feature models. The discrepancy between measured and modeled values decreases by 12% after taking into account straylight effects on PSPT images. PRD computations on either the most recent or the earlier atmosphere models of bright features reproduce measurements from plage and bright plage regions with a similar accuracy.Comment: 14 pages, 18 figures, accepted by A&

The existence of the Lambda effect in the solar convection zone indicated by SDO observations

The empirical finding with data from the Solar Dynamics Observatory (SDO) of positive (negative) horizontal Reynolds stress at the northern (southern) hemisphere for solar giant cells (Hathaway et al. 2013) is discussed for its consequences for the theory of the solar/stellar differential rotation. Solving the nonlinear Reynolds equation for the angular velocity under neglect of the meridional circulation we show that the horizontal Reynolds stress of the northern hemisphere is always negative at the surface but it is positive in the bulk of the solar convection zone by the action of the Lambda effect. The Lambda effect, which describes the angular momentum transport of rigidly rotating anisotropic turbulence and which avoids a rigid-body rotation of the convection zones, is in horizontal direction of cubic power in the rotation rate $\Omega$ and it is always equatorwards directed. Theories without Lambda effect which may also provide the observed solar rotation law only by the action of a meridional circulation lead to a horizontal Reynolds stress with the opposite sign as observed.Comment: 4 pages, 6 figure

Diversifying Anaerobic Respiration Strategies to Compete in the Rhizosphere

The rhizosphere is the interface between plant roots and soil where intense, varied interactions between plants and microbes influence plants' health and growth through their influence on biochemical cycles, such as the carbon, nitrogen, and iron cycles. The rhizosphere is also a changing environment where oxygen can be rapidly limited and anaerobic zones can be established. Microorganisms successfully colonize the rhizosphere when they possess specific traits referred to as rhizosphere competence. Anaerobic respiration flexibility contributes to the rhizosphere competence of microbes. Indeed, a wide range of compounds that are available in the rhizosphere can serve as alternative terminal electron acceptors during anaerobic respiration such as nitrates, iron, carbon compounds, sulfur, metalloids, and radionuclides. In the presence of multiple terminal electron acceptors in a complex environment such as the rhizosphere and in the absence of O2, microorganisms will first use the most energetic option to sustain growth. Anaerobic respiration has been deeply studied, and the genes involved in anaerobic respiration have been identified. However, aqueous environment and paddy soils are the most studied environments for anaerobic respiration, even if we provide evidence in this review that anaerobic respiration also occurs in the plant rhizosphere. Indeed, we provide evidence by performing a BLAST analysis on metatranscriptomic data that genes involved in iron, sulfur, arsenate and selenate anaerobic respiration are expressed in the rhizosphere, underscoring that the rhizosphere environment is suitable for the establishment of anaerobic respiration. We thus focus this review on current research concerning the different types of anaerobic respiration that occur in the rhizosphere. We also discuss the flexibility of anaerobic respiration as a fundamental trait for the microbial colonization of roots, environmental and ecological adaptation, persistence and bioremediation in the rhizosphere. Anaerobic respiration appears to be a key process for the functioning of an ecosystem and interactions between plants and microbes

Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators

Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition. First, we show that a low-rank density matrix can be estimated using fewer copies of the state, i.e., the sample complexity of tomography decreases with the rank. Second, we show that unknown low-rank states can be reconstructed from an incomplete set of measurements, using techniques from compressed sensing and matrix completion. These techniques use simple Pauli measurements, and their output can be certified without making any assumptions about the unknown state. We give a new theoretical analysis of compressed tomography, based on the restricted isometry property (RIP) for low-rank matrices. Using these tools, we obtain near-optimal error bounds, for the realistic situation where the data contains noise due to finite statistics, and the density matrix is full-rank with decaying eigenvalues. We also obtain upper-bounds on the sample complexity of compressed tomography, and almost-matching lower bounds on the sample complexity of any procedure using adaptive sequences of Pauli measurements. Using numerical simulations, we compare the performance of two compressed sensing estimators with standard maximum-likelihood estimation (MLE). We find that, given comparable experimental resources, the compressed sensing estimators consistently produce higher-fidelity state reconstructions than MLE. In addition, the use of an incomplete set of measurements leads to faster classical processing with no loss of accuracy. Finally, we show how to certify the accuracy of a low rank estimate using direct fidelity estimation and we describe a method for compressed quantum process tomography that works for processes with small Kraus rank.Comment: 16 pages, 3 figures. Matlab code included with the source file