Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs

We present two realistic entanglement concentration protocols (ECPs) for pure partially entangled photons. A partially entangled photon pair can be concentrated to a maximally entangled pair with only an ancillary single photon in a certain probability, while the conventional ones require two copies of partially entangled pairs at least. Our first protocol is implemented with linear optics and the second one is implemented with cross-Kerr nonlinearities. Compared with other ECPs, they do not need to know the accurate coefficients of the initial state. With linear optics, it is feasible with current experiment. With cross-Kerr nonlinearities, it does not require the sophisticated single-photon detectors and can be repeated to get a higher success probability. Moreover, the second protocol can get the higher entanglement transformation efficiency and it maybe the most economical one by far. Meanwhile, both of protocols are more suitable for multi-photon system concentration, because they need less operations and classical communications. All these advantages make two protocols be useful in current long-distance quantum communications

The largest virialized dark halo in the universe

Using semi-analytic approach, we present an estimate of the properties of the largest virialized dark halos in the present universe for three different scenarios of structure formation: SCDM, LCDM and OCDM models. The resulting virial mass and temperature increase from the lowest values of $1.6 \times 10^{15}h^{-1}M_{\odot}$ and 9.8 keV in OCDM, the mid-range values of $9.0 \times 10^{15}h^{-1}M_{\odot}$ and 31 keV in LCDM, to the highest values of $20.9 \times 10^{15}h^{-1}M_{\odot}$, 65 keV in SCDM. As compared with the largest virialized object seen in the universe, the richest clusters of galaxies, we can safely rule out the OCDM model. In addition, the SCDM model is very unlikely because of the unreasonably high virial mass and temperature. Our computation favors the prevailing LCDM model in which superclusters may be marginally regarded as dynamically-virialized systems.Comment: 5 pages, Accepted by Int. J. Mod. Phys.