Multiparameter estimation in networked quantum sensors

We introduce a general model for a network of quantum sensors, and we use this model to consider the following question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. This immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or nonlinear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network

The Relation Between Galaxy ISM and Circumgalactic OVI Gas Kinematics Derived from Observations and Λ\LambdaCDM Simulations

We present the first galaxy-OVI absorption kinematic study for 20 absorption systems (EW>0.1~{\AA}) associated with isolated galaxies (0.15$<z<$0.55) that have accurate redshifts and rotation curves obtained using Keck/ESI. Our sample is split into two azimuthal angle bins: major axis ($\Phi<25^{\circ}$) and minor axis ($\Phi>33^{\circ}$). OVI absorption along the galaxy major axis is not correlated with galaxy rotation kinematics, with only 1/10 systems that could be explained with rotation/accretion models. This is in contrast to co-rotation commonly observed for MgII absorption. OVI along the minor axis could be modeled by accelerating outflows but only for small opening angles, while the majority of the OVI is decelerating. Along both axes, stacked OVI profiles reside at the galaxy systemic velocity with the absorption kinematics spanning the entire dynamical range of their galaxies. The OVI found in AMR cosmological simulations exists within filaments and in halos of ~50 kpc surrounding galaxies. Simulations show that major axis OVI gas inflows along filaments and decelerates as it approaches the galaxy while increasing in its level of co-rotation. Minor axis outflows in the simulations are effective within 50-75 kpc beyond that they decelerate and fall back onto the galaxy. Although the simulations show clear OVI kinematic signatures they are not directly comparable to observations. When we compare kinematic signatures integrated through the entire simulated galaxy halo we find that these signatures are washed out due to full velocity distribution of OVI throughout the halo. We conclude that OVI alone does not serve as a useful kinematic indicator of gas accretion, outflows or star-formation and likely best probes the halo virial temperature.Comment: 24 pages, 21 figures, 4 tables. Accepted to ApJ on November 14, 201

Mixtures in non stable Levy processes

We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that -- at least for one particular type of Student processes suggested by recent empirical results, and for integral times -- the distribution of the process is a mixture of other types of Student distributions, randomized by means of a new probability distribution. The mixture is such that along the time the asymptotic behavior of the probability density functions always coincide with that of the generating Student law. We put forward the conjecture that this can be a general feature of the Student processes. We finally analyze the Ornstein--Uhlenbeck process driven by our Levy noises and show a few simulation of it.Comment: 28 pages, 3 figures, to be published in J. Phys. A: Math. Ge

Feller Processes: The Next Generation in Modeling. Brownian Motion, L\'evy Processes and Beyond

We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of L\'evy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also L\'evy processes, of which Brownian Motion is a special case, have become increasingly popular. L\'evy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include L\'evy processes and in particular Brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.Comment: 22 pages, including 4 figures and 8 pages of source code for the generation of sample paths of Feller processe

Assessing the Cognitive Translational Potential of a Mouse Model of the 22q11.2 Microdeletion Syndrome.

A chromosomal microdeletion at the 22q11.2 locus is associated with extensive cognitive impairments, schizophrenia and other psychopathology in humans. Previous reports indicate that mouse models of the 22q11.2 microdeletion syndrome (22q11.2DS) may model the genetic basis of cognitive deficits relevant for neuropsychiatric disorders such as schizophrenia. To assess the models usefulness for drug discovery, a novel mouse (Df(h22q11)/+) was assessed in an extensive battery of cognitive assays by partners within the NEWMEDS collaboration (Innovative Medicines Initiative Grant Agreement No. 115008). This battery included classic and touchscreen-based paradigms with recognized sensitivity and multiple attempts at reproducing previously published findings in 22q11.2DS mouse models. This work represents one of the most comprehensive reports of cognitive functioning in a transgenic animal model. In accordance with previous reports, there were non-significant trends or marginal impairment in some tasks. However, the Df(h22q11)/+ mouse did not show comprehensive deficits; no robust impairment was observed following more than 17 experiments and 14 behavioral paradigms. Thus - within the current protocols - the 22q11.2DS mouse model fails to mimic the cognitive alterations observed in human 22q11.2 deletion carriers. We suggest that the 22q11.2DS model may induce liability for cognitive dysfunction with additional "hits" being required for phenotypic expression.The research leading to these results has received support from the Innovative Medicine Initiative Joint Undertaking under grant agreement No. 115008 of which resources are composed of EFPIA in-kind contribution and financial contribution from the European Union’s Seventh Framework Programme (FP7/ 2007–2013). The Behavioural and Clinical Neuroscience Institute is co-funded by the Medical Research Council and the Df(h22q11)/+ and the Wellcome Trust.This is the final version of the article. It first appeared from OUP at http://dx.doi.org/10.1093/cercor/bhw229

Defining management units for cetaceans by combining genetics, morphology, acoustics and satellite tracking

Managing animal units is essential in biological conservation and requires spatial and temporal identification of such units. Since even neighbouring populations often have different conservation status and face different levels of anthropogenic pressure, detailed knowledge of population structure, seasonal range and overlap with animals from neighbouring populations is required to manage each unit separately. Previous studies on genetic structure and morphologic separation suggests three distinct populations of harbour porpoises with limited geographic overlap in the North Sea (NS), the Belt Sea (BS) and the Baltic Proper (BP) region. In this study, we aim to identify a management unit for the BS population of harbour porpoises. We use Argos satellite data and genetics from biopsies of tagged harbour porpoises as well as acoustic data from 40 passive acoustic data loggers to determine management areas with the least overlap between populations and thus the least error when abundance and population status is estimated. Discriminant analysis of the satellite tracking data from the BS and NS populations showed that the best fit of the management unit border during the summer months was an east–west line from Denmark to Sweden at latitude 56.95°N. For the border between BS and BP, satellite tracking data indicate a sharp decline in population density at 13.5°E, with 90% of the locations being west of this line. This was supported by the acoustic data with the average daily detection rate being 27.5 times higher west of 13.5°E as compared to east of 13.5°E. By using this novel multidisciplinary approach, we defined a management unit for the BS harbour porpoise population. We recommend that these boundaries are used for future monitoring efforts of this population under the EU directives. The boundaries may also be used for conservation efforts during the summer months, while seasonal movements of harbour porpoises should be considered during winter

Erratum : Anyon braiding on a fractal lattice with a local Hamiltonian (Physical Review A (2022) 105 (L021302) DOI: 10.1103/PhysRevA.105.L021302)

There is a growing interest in searching for topology in fractal dimensions with the aim of finding different properties and advantages compared to the integer dimensional case. Here, we construct a local Hamiltonian on a fractal lattice whose ground state exhibits topological braiding properties. The fractal lattice is obtained from a second generation Sierpinski carpet with Hausdorff dimension 1.89. We use local potentials to trap and exchange anyons in the model, and the numerically obtained results for the exchange statistics of the anyons are close to the ideal statistics for quasiholes in a bosonic Laughlin state at half filling. For the considered system size, the energy gap is about three times larger for the fractal lattice than for a two-dimensional square lattice, and we find that the braiding results obtained on the fractal lattice are more robust against disorder. We propose a scheme to implement both fractal lattices and our proposed local Hamiltonian with ultracold atoms in optical lattices