A volume inequality for quantum Fisher information and the uncertainty principle

Let $A_1,...,A_N$ be complex self-adjoint matrices and let $\rho$ be a density matrix. The Robertson uncertainty principle $$det(Cov_\rho(A_h,A_j)) \geq det(- \frac{i}{2} Tr(\rho [A_h,A_j]))$$ gives a bound for the quantum generalized covariance in terms of the commutators $[A_h,A_j]$. The right side matrix is antisymmetric and therefore the bound is trivial (equal to zero) in the odd case $N=2m+1$. Let $f$ be an arbitrary normalized symmetric operator monotone function and let $_{\rho,f}$ be the associated quantum Fisher information. In this paper we conjecture the inequality $$det (Cov_\rho(A_h,A_j)) \geq det (\frac{f(0)}{2} _{\rho,f})$$ that gives a non-trivial bound for any natural number $N$ using the commutators $i[\rho, A_h]$. The inequality has been proved in the cases $N=1,2$ by the joint efforts of many authors. In this paper we prove the case N=3 for real matrices

Novel thick-foam ferroelectret with engineered voids for energy harvesting applications

This work reports a novel thick-foam ferroelectret which is designed and engineered for energy harvesting applications. We fabricated this ferroelectret foam by mixing a chemical blowing agent with a polymer solution, then used heat treatment to activate the agent and create voids in the polymer foam. The dimensions of the foam, the density and size of voids can be well controlled in the fabrication process. Therefore, this ferroelectret can be engineered into optimized structure for energy harvesting applications

CDC42 and Rac1 control different actin-dependent processes in the Drosophila wing disc epithelium.

Cdc42 and Rac1 are members of the rho family of small guanosinetriphosphatases and are required for a diverse set of cytoskeleton-membrane interactions in different cell types. Here we show that these two proteins contribute differently to the organization of epithelial cells in the Drosophila wing imaginal disc. Drac1 is required to assemble actin at adherens junctions. Failure of adherens junction actin assembly in Drac1 dominant-negative mutants is associated with increased cell death. Dcdc42, on the other hand, is required for processes that involve polarized cell shape changes during both pupal and larval development. In the third larval instar, Dcdc42 is required for apico-basal epithelial elongation. Whereas normal wing disc epithelial cells increase in height more than twofold during the third instar, cells that express a dominant-negative version of Dcdc42 remain short and are abnormally shaped. Dcdc42 localizes to both apical and basal regions of the cell during these events, and mediates elongation, at least in part, by effecting a reorganization of the basal actin cytoskeleton. These observations suggest that a common cdc42-based mechanism may govern polarized cell shape changes in a wide variety of cell types

Metric adjusted skew information: Convexity and restricted forms of superadditivity

We give a truly elementary proof of the convexity of metric adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric adjusted skew informations. Recently, Luo and Zhang introduced the notion of semi-quantum states on a bipartite system and proved superadditivity of the Wigner-Yanase-Dyson skew informations for such states. We extend this result to general metric adjusted skew informations. We finally show that a recently introduced extension to parameter values $1<p\le 2$ of the WYD-information is a special case of (unbounded) metric adjusted skew information.Comment: An error in the literature is pointed ou

Improved lattice QCD with quarks: the 2 dimensional case

QCD in two dimensions is investigated using the improved fermionic lattice Hamiltonian proposed by Luo, Chen, Xu, and Jiang. We show that the improved theory leads to a significant reduction of the finite lattice spacing errors. The quark condensate and the mass of lightest quark and anti-quark bound state in the strong coupling phase (different from t'Hooft phase) are computed. We find agreement between our results and the analytical ones in the continuum.Comment: LaTeX file (including text + 10 figures

Ultraviolet/X-ray variability and the extended X-ray emission of the radio-loud broad absorption line quasar PG 1004+130

We present the results of recent Chandra, XMM-Newton, and Hubble Space Telescope observations of the radio-loud (RL), broad absorption line (BAL) quasar PG 1004+130. We compare our new observations to archival X-ray and UV data, creating the most comprehensive, high signal-to-noise, multi-epoch, spectral monitoring campaign of a RL BAL quasar to date. We probe for variability of the X-ray absorption, the UV BAL, and the X-ray jet, on month-year timescales. The X-ray absorber has a low column density of $N_{H}=8\times10^{20}-4\times10^{21}$ cm$^{-2}$ when it is assumed to be fully covering the X-ray emitting region, and its properties do not vary significantly between the 4 observations. This suggests the observed absorption is not related to the typical "shielding gas" commonly invoked in BAL quasar models, but is likely due to material further from the central black hole. In contrast, the CIV BAL shows strong variability. The equivalent width (EW) in 2014 is EW=11.24$\pm$0.56 \AA, showing a fractional increase of $\Delta EW / \langle EW \rangle$=1.16$\pm$0.11 from the 2003 observation, 3183 days earlier in the rest-frame. This places PG 1004+130 among the most highly variable BAL quasars. By combining Chandra observations we create an exposure 2.5 times deeper than studied previously, with which to investigate the nature of the X-ray jet and extended diffuse X-ray emission. An X-ray knot, likely with a synchrotron origin, is detected in the radio jet ~8 arcsec (30 kpc) from the central X-ray source with a spatial extent of ~4 arcsec (15 kpc). No similar X-ray counterpart to the counterjet is detected. Asymmetric, non-thermal diffuse X-ray emission, likely due to inverse Compton scattering of Cosmic Microwave Background photons, is also detected.Comment: 15 pages, 7 figures, 3 tables. Accepted for publication in Ap

Geometric discord and Measurement-induced nonlocality for well known bound entangled states

We employ geometric discord and measurement induced nonlocality to quantify non classical correlations of some well-known bipartite bound entangled states, namely the two families of Horodecki's ($2\otimes 4$, $3\otimes 3$ and $4\otimes 4$ dimensional) bound entangled states and that of Bennett etal's in $3\otimes 3$ dimension. In most of the cases our results are analytic and both the measures attain relatively small value. The amount of quantumness in the $4\otimes 4$ bound entangled state of Benatti etal and the $2\otimes 8$ state having the same matrix representation (in computational basis) is same. Coincidently, the $2m\otimes 2m$ Werner and isotropic states also exhibit the same property, when seen as $2\otimes 2m^2$ dimensional states.Comment: V2: Title changed, one more state added; 11 pages (single column), 2 figures, accepted in Quantum Information Processin

Disordered Kondo Nanoclusters: Effect of Energy Spacing

Exact diagonalization results for Kondo nanoclusters alloyed with mixed valence impurities show that tuning the {\it energy spacing}, $\Delta$, drives the system from the Kondo to the RKKY regime. The interplay of $\Delta$ and disorder gives rise to a $\Delta$ versus concentration T=0 phase diagram very rich in structure, where regions with prevailing Kondo or RKKY correlations alternate with domains of ferromagnetic order. The local Kondo temperatures, $T_K$, and RKKY interactions depend strongly on the local environment and are overall {\it enhanced} by disorder, in contrast to the hypothesis of ``Kondo disorder'' single-impurity models.Comment: 4pages 4 figuresDisordered Kondo Nanoclusters: Effect of Energy Spacin