Entanglement requirements for implementing bipartite unitary operations

We prove, using a new method based on map-state duality, lower bounds on entanglement resources needed to deterministically implement a bipartite unitary using separable (SEP) operations, which include LOCC (local operations and classical communication) as a particular case. It is known that the Schmidt rank of an entangled pure state resource cannot be less than the Schmidt rank of the unitary. We prove that if these ranks are equal the resource must be uniformly (maximally) entangled: equal nonzero Schmidt coefficients. Higher rank resources can have less entanglement: we have found numerical examples of Schmidt rank 2 unitaries which can be deterministically implemented, by either SEP or LOCC, using an entangled resource of two qutrits with less than one ebit of entanglement.Comment: 7 pages Revte

Modelling SDG scenarios for Educational Attainment and Development. CESDEG: Education for all Global Monitoring Report (EFA-GMR)

The scenarios of educational expansion underlying the population projections presented here result from a further refinement of the education model presented in Lutz et al. (2014). In summary, we project the share of the population ever reaching or exceeding a given attainment level. This is done seperately by country, and gender, but with ‘shrinkage’ within a Bayesian framework (with weakly informative priors). The mean expansion trajectories are modelled as random walks with drift (and potential mean reversion) and independent noise at a probit-transformed scale. The trend parameters are estimated based on reconstructed attainment histories, and extrapolated, subject to additional and some exogenously imposed convergence within regions and between females and males. Under the target scenarios, SDG targets are treated as ‘future data’ (in other words, target trajectories are modeled looking back from 2030 under the assumption that the target will have been met), with a potential trend break in 2015. Limitations shared with all existing global projections of educational development include the fact that in the absence of a detailed theoretical basis, they are forced to rely heavily on statistical extrapolations. For example, there is little consensus on whether “higher education is the new secondary education” (as claimed by Andreas Schleicher of OECD), or is fundamentally different from lower levels of schooling (e.g. in terms of institutional framework, its role in the life cycle, economic returns. In addition, global projections can necessarily not account in a satisfactory manner for idiosyncratic policy changes or shocks. In addition, the specific modelling choices outlined above imply a number of trade-offs. Using highest school attainment as the underlying measure solves many problems associated with historic enrolment data by allowing the consistent reconstruction of time series of attainment from relatively recent cross-sectional data, but comes with challenges of its own. While nevertheless preferable overall, the principal disadvantage of attainment measures deserves mention, namely the relatively long time lag with which outcomes can be observed. Late attainment is common in many developing countries, so that attainment cannot safely be assumed to be ‘final’ until several years above the typical graduation age

Does export dependency hurt economic development? Empirical evidence from Singapore

A rapid export growth in East Asia was once identified as a source of the sustainable economic development that the region enjoyed. However, the current global recession has turned exports from an economic virtue to a vice. There is a growing awareness that a heavy reliance on exports has caused a serious economic downturn in the region. The present paper chooses Singapore as a case study to examine the relationship between the origin of the East Asian Miracle (i.e. export dependency) and the economic growth. For this purpose, the study employs a causality test developed by Toda and Yamamoto. The empirical findings indicate that despite a negative long-run relationship between export dependency and economic growth, Singapore's heavy reliance on exports does not seem to have produced negative effects on the nation's economic growth. This is because the increase in export dependency was an effect, and not a cause, of the country's output expansion.

Microscopic Origin of Quantum Chaos in Rotational Damping

The rotational spectrum of $^{168}$Yb is calculated diagonalizing different effective interactions within the basis of unperturbed rotational bands provided by the cranked shell model. A transition between order and chaos taking place in the energy region between 1 and 2 MeV above the yrast line is observed, associated with the onset of rotational damping. It can be related to the higher multipole components of the force acting among the unperturbed rotational bands.Comment: 7 pages, plain TEX, YITP/K-99

U-duality covariant membranes

We outline a formulation of membrane dynamics in D=8 which is fully covariant under the U-duality group SL(2,Z) x SL(3,Z), and encodes all interactions to fields in the eight-dimensional supergravity, which is constructed through Kaluza-Klein reduction on T^3. Among the membrane degrees of freedom is an SL(2,R) doublet of world-volume 2-form potentials, whose quantised electric fluxes determine the membrane charges, and are conjectured to provide an interpretation of the variables occurring in the minimal representation of E_{6(6)} which appears in the context of automorphic membranes. We solve the relevant equations for the action for a restricted class of supergravity backgrounds. Some comments are made on supersymmetry and lower dimensions.Comment: LaTeX, 21 pages. v2: Minor changes in text, correction of a sign. v3: some changes in text, a sign convention changed; version to appear in JHE

Direct measurement of S-branch N(2)-H(2) Raman linewidths using time-resolved pure rotational coherent anti-Stokes Raman spectroscopy.

S-branch N(2)-H(2) Raman linewidths have been measured in the temperature region 294-1466 K using time-resolved dual-broadband picosecond pure rotational coherent anti-Stokes Raman spectroscopy (RCARS). Data are extracted by mapping the dephasing rates of the CARS signal temporal decay. The J-dependent coherence decays are detected in the time domain by following the individual spectral lines as a function of probe delay. The linewidth data set was employed in spectral fits of N(2) RCARS spectra recorded in binary mixtures of N(2) and H(2) at calibrated temperature conditions up to 661 K using a standard nanosecond RCARS setup. In this region, the set shows a deviation of less than 2% in comparison with thermocouples. The results provide useful knowledge for the applicability of N(2) CARS thermometry on the fuel-side of H(2) diffusion flames

Light from Cascading Partons in Relativistic Heavy-Ion Collisions

We calculate the production of high energy photons from Compton and annihilation processes as well as fragmentation off quarks in the parton cascade model. The multiple scattering of partons is seen to lead to a substantial production of high energy photons, which rises further when parton multiplication due to final state radiation is included. The photon yield is found to be proportional to the number of collisions among the cascading partons.Comment: revised version: 4 pages, 4 figures, uses REVTEX

Supersymmetry and Generic BSM Models in PYTHIA 8

We describe the implementation of supersymmetric models in PYTHIA 8, including production and decay of superparticles and allowing for violation of flavour, CP, and R-parity. We also present a framework for importing generic new-physics matrix elements into PYTHIA 8, in a way suitable for use with automated tools. We emphasize that this possibility should not be viewed as the only way to implement new-physics models in PYTHIA 8, but merely as an additional possibility on top of the already existing ones. Finally we address parton showers in exotic colour topologies, in particular ones involving colour epsilon tensors and colour sextets.Comment: 20 page

Summing free unitary random matrices

I use quaternion free probability calculus - an extension of free probability to non-Hermitian matrices (which is introduced in a succinct but self-contained way) - to derive in the large-size limit the mean densities of the eigenvalues and singular values of sums of independent unitary random matrices, weighted by complex numbers. In the case of CUE summands, I write them in terms of two "master equations," which I then solve and numerically test in four specific cases. I conjecture a finite-size extension of these results, exploiting the complementary error function. I prove a central limit theorem, and its first sub-leading correction, for independent identically-distributed zero-drift unitary random matrices.Comment: 17 pages, 15 figure