Construction of optimal witness for unknown two-qubit entanglement

Whether entanglement in a state can be detected, distilled, and quantified without full state reconstruction is a fundamental open problem. We demonstrate a new scheme encompassing these three tasks for arbitrary two-qubit entanglement, by constructing the optimal entanglement witness for polarization-entangled mixed-state photon pairs without full state reconstruction. With better efficiency than quantum state tomography, the entanglement is maximally distilled by newly developed tunable polarization filters, and quantified by the expectation value of the witness, which equals the concurrence. This scheme is extendible to multiqubit Greenberger-Horne-Zeilinger entanglement.Comment: Phys. Rev. Lett. 105, 230404 (2010); supplementary information (OWitness_sup.pdf) is included in source zip fil

Newly discovered brown dwarfs not seen in microlensing time scale frequency distribution?

The 2-Micron All Sky Survey (2MASS) (Skrutskie et al. 1997) and the DEep Near Infrared Survey of the southern sky (DENIS) (Epchtein et al. 1997) have revealed a heretofore unknown population of free brown dwarfs that has extended the local mass function down to as small as 0.01M_sun (Reid et al. 1999). If this local proportion of brown dwarfs extends throughout the Galaxy---in particular in the Galactic bulge---one expects an increase in the predicted fraction of short time scale microlensing events in directions toward the Galactic bulge. Zhao et al.(1996) have indicated that a mass function with 30-60% of the lens mass in brown dwarfs is not consistent with empirical microlensing data. Here we show that even the much lower mass fraction (~ 10%) of brown dwarfs inferred from the new discoveries appears inconsistent with the data. The added brown dwarfs do indeed increase the expected number of short time scale events, but they appear to drive the peak in the time scale frequency distribution to time scales smaller than that observed, and do not otherwise match the observed distribution. A reasonably good match to the empirical data (Alcock et al. 1996) is obtained by increasing the fraction of stars in the range 0.08<m<0.7M_sun considerably above that deduced from several star counts. However, all inferences from microlensing about the appropriate stellar mass function must be qualified by the meagerness of the microlensing data and the uncertainties in the Galactic model.Comment: 5 pages, 1 figure. PS file using aas2pp4.sty. To appear in ApJ Letter

On quantum vertex algebras and their modules

We give a survey on the developments in a certain theory of quantum vertex algebras, including a conceptual construction of quantum vertex algebras and their modules and a connection of double Yangians and Zamolodchikov-Faddeev algebras with quantum vertex algebras.Comment: 18 pages; contribution to the proceedings of the conference in honor of Professor Geoffrey Maso

Probability of Detecting a Planetary Companion during a Microlensing Event

The probability of detecting a planetary companion of a lensing star during a microlensing event toward the Galactic center, averaged over all relevant event and galactic parameters, when the planet-star mass ratio $q=0.001$ has a maximum exceeding 10% at an orbit semimajor axis $a$ near 1.5 AU for a uniform distribution of impact parameters. The maximum probability is raised to more than 20% for a distribution of source-lens impact parameters that is determined by the efficiency of event detection. The averaging procedures are carefully defined, and they determinine the dependence of the detection probabilities on several properties of the Galaxy. The probabilities scale approximately as $\sqrt{q}$. A planet is assumed detectable if the perturbation of the single lens light curve exceeds $2/(S/N)$ for at least 20 consecutive photometric points sometime during the event. Two meter telescopes with 60 second integrations in I-band with high time resolution photometry throughout the duration of an ongoing event are assumed. The probabilities are derived as a function of $a$, where they remain significant for $0.6<a<10$ AU. Dependence of the detection probabilities on the lens mass function, luminosity function of the source stars as modified by extinction, distribution of source-lens impact parameters, and the line of sight to the source are also determined, and the probabilities are averaged over the distribution of the projected planet position, the lens mass function, the distribution of impact parameters, the lens and source distances as weighted by their distributions along the line of sight and over the $I$-band apparent luminosity function of the sources. The extraction of the probabilility as a function of $a$ for a particular $q$ from empirical data is indicated.Comment: 32 pages, 20 figures, In Press, ApJ, Latex format with aas2pp4 forma

System Size Stochastic Resonance: General Nonequilibrium Potential Framework

We study the phenomenon of system size stochastic resonance within the nonequilibrium potential's framework. We analyze three different cases of spatially extended systems, exploiting the knowledge of their nonequilibrium potential, showing that through the analysis of that potential we can obtain a clear physical interpretation of this phenomenon in wide classes of extended systems. Depending on the characteristics of the system, the phenomenon results to be associated to a breaking of the symmetry of the nonequilibrium potential or to a deepening of the potential minima yielding an effective scaling of the noise intensity with the system size.Comment: LaTex, 24 pages and 9 figures, submitted to Phys. Rev.