A characterization of positive linear maps and criteria of entanglement for quantum states

Let $H$ and $K$ be (finite or infinite dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from ${\mathcal B}(H)$ into ${\mathcal B}(K)$ is given, which particularly gives a characterization of positive elementary operators including all positive linear maps between matrix algebras. This characterization is then applied give a representation of quantum channels (operations) between infinite-dimensional systems. A necessary and sufficient criterion of separability is give which shows that a state $\rho$ on $H\otimes K$ is separable if and only if $(\Phi\otimes I)\rho\geq 0$ for all positive finite rank elementary operators $\Phi$. Examples of NCP and indecomposable positive linear maps are given and are used to recognize some entangled states that cannot be recognized by the PPT criterion and the realignment criterion.Comment: 20 page

The spectral energy distribution of galaxies at z > 2.5: Implications from the Herschel/SPIRE color-color diagram

We use the Herschel SPIRE color-color diagram to study the spectral energy distribution (SED) and the redshift estimation of high-z galaxies. We compiled a sample of 57 galaxies with spectroscopically confirmed redshifts and SPIRE detections in all three bands at $z=2.5-6.4$, and compared their average SPIRE colors with SED templates from local and high-z libraries. We find that local SEDs are inconsistent with high-z observations. The local calibrations of the parameters need to be adjusted to describe the average colors of high-z galaxies. For high-z libraries, the templates with an evolution from z=0 to 3 can well describe the average colors of the observations at high redshift. Using these templates, we defined color cuts to divide the SPIRE color-color diagram into different regions with different mean redshifts. We tested this method and two other color cut methods using a large sample of 783 Herschel-selected galaxies, and find that although these methods can separate the sample into populations with different mean redshifts, the dispersion of redshifts in each population is considerably large. Additional information is needed for better sampling.Comment: 17 pages, 14 figures, accepted for publication in A&

Fermi resonance-algebraic model for molecular vibrational spectra

A Fermi resonance-algebraic model is proposed for molecular vibrations, where a U(2) algebra is used for describing the vibrations of each bond, and Fermi resonances between stretching and bending modes are taken into account. The model for a bent molecule XY_2 and a molecule XY_3 is successfully applied to fit the recently observed vibrational spectrum of the water molecule and arsine (AsH_3), respectively, and results are compared with those of other models. Calculations show that algebraic approaches can be used as an effective method for describing molecular vibrations with small standard deviations

Tevatron Mass Limits for Heavy Quarks Decaying via Flavor Changing Neutral Current

The dimuon and dielectron data from the Tevatron $\bar pp$ collider are used to probe for heavy quarks, which decay dominantly via flavour changing neutral current. Depending on whether the $FCNC$ decay occurs at the tree or loop level, one gets a lower mass limit of 85 or 75 GeV. The former applies to singlet, vector doublet and mirror type quarks while the latter applies to a lefthanded quark doublet of the fourth generation.Comment: 13 pages, TIFR/TH/92-58, Two figures to be supplied on reques

Two-qubit Quantum Logic Gate in Molecular Magnets

We proposed a scheme to realize a controlled-NOT quantum logic gate in a dimer of exchange coupled single-molecule magnets, $[\textrm{Mn}_4]_2$. We chosen the ground state and the three low-lying excited states of a dimer in a finite longitudinal magnetic field as the quantum computing bases and introduced a pulsed transverse magnetic field with a special frequency. The pulsed transverse magnetic field induces the transitions between the quantum computing bases so as to realize a controlled-NOT quantum logic gate. The transition rates between the quantum computing bases and between the quantum computing bases and other excited states are evaluated and analyzed.Comment: 7 pages, 2 figure

Experimental Distillation of Quantum Nonlocality

We report the first experimental demonstration of distillation of quantum nonlocality, confirming the recent theoretical protocol [\textit{Phys. Rev. Lett. 102, 120401 (2009)}]. Quantum nonlocality is described by a correlation box with binary inputs and outputs, and the nonlocal boxes are realized through appropriate measurements on polarization entangled photon pairs. We demonstrate that nonlocality is amplified by connecting two nonlocal boxes into a composite one through local operations and four-photon coincidence measurements

Charmless Three-Body Baryonic B Decays

Motivated by recent data on B-> p pbar K decay, we study various charmless three-body baryonic B decay modes, including Lambda pbar pi, Sigma0 pbar pi, p pbar pi, p pbar Kbar0, in a factorization approach. These modes have rates of order 10^{-6}. There are two mechanisms for the baryon pair production, current-produced and transition. The behavior of decay spectra from these baryon production mechanisms can be understood by using QCD counting rules. Predictions on rates and decay spectra can be checked in the near future.Comment: 26 pages, 9 figures; version to appear in Phys. Rev.

Effects of tai chi on postural control during dual-task stair negotiation in knee osteoarthritis : a randomised controlled trial protocol

Stair ascent and descent require complex integration between sensory and motor systems; individuals with knee osteoarthritis (KOA) have an elevated risk for falls and fall injuries, which may be in part due to poor dynamic postural control during locomotion. Tai chi exercise has been shown to reduce fall risks in the ageing population and is recommended as one of the non-pharmocological therapies for people with KOA. However, neuromuscular mechanisms underlying the benefits of tai chi for persons with KOA are not clearly understood. Postural control deficits in performing a primary motor task may be more pronounced when required to simultaneously attend to a cognitive task. This single-blind, parallel design randomised controlled trial (RCT) aims to evaluate the effects of a 12-week tai chi programme versus balance and postural control training on neuromechanical characteristics during dual-task stair negotiation. Sixty-six participants with KOA will be randomised into either tai chi or balance and postural control training, each at 60 min per session, twice weekly for 12 weeks. Assessed at baseline and 12 weeks (ie, postintervention), the primary outcomes are attention cost and dynamic postural stability during dual-task stair negotiation. Secondary outcomes include balance and proprioception, foot clearances, self-reported symptoms and function. A telephone follow-up to assess symptoms and function will be conducted at 20 weeks. The findings will help determine whether tai chi is beneficial on dynamic stability and in reducing fall risks in older adults with KOA patients in community. Ethics approval was obtained from the Ethics Committee of the Affiliated Rehabilitation Hospital of Fujian University of Traditional Chinese Medicine (#2018KY-006-1). Study findings will be disseminated through presentations at scientific conferences or publications in peer-reviewed journals. ChiCTR1800018028. [Abstract copyright: © Author(s) (or their employer(s)) 2020. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.

A hard metallic material: Osmium Diboride

We calculate the structural and electronic properties of OsB2 using density functional theory with or without taking into account spin-orbit (SO) interaction. Our results show that the bulk modulus with and without SO interaction are 364 and 365 Gpa respectively, both are in good agreement with experiment (365-395 Gpa). The evidence of covalent bonding of Os-B, which plays an important role to form a hard material, is indicated both in charge density, atoms in molecules analysis, and density of states analysis. The good metallicity and hardness of OsB2 might suggest its potential application as hard conductors.Comment: Figures improve