Cocycle deformations and Galois objects of semisimple Hopf algebras of dimension 1616

In this article, we determine cocycle deformations and Galois objects of non-commutative and non-cocommutative semisimple Hopf algebras of dimension $16$. We show that these Hopf algebras are pairwise twist inequivalent mainly by calculating their higher Frobenius-Schur indicators, and that except three Hopf algebras which are cocycle deformations of dual group algebras, none of them admit non-trivial cocycle deformations.Comment: 22 page

Quasi Distribution Amplitude of Heavy Quarkonia

The recently-proposed quasi distributions point out a promising direction for lattice QCD to investigate the light-cone correlators, such as parton distribution functions (PDF) and distribution amplitudes (DA), directly in the $x$-space. Owing to its excessive simplicity, the heavy quarkonium can serve as an ideal theoretical laboratory to ascertain certain features of quasi-DA. In the framework of non-relativistic QCD (NRQCD) factorization, we compute the order-$\alpha_s$ correction to both light-cone distribution amplitudes (LCDA) and quasi-DA associated with the lowest-lying quarkonia, with the transverse momentum UV cutoff interpreted as the renormalization scale. We confirm analytically that the quasi-DA of a quarkonium does reduce to the respective LCDA in the infinite-momentum limit. We also observe that, provided that the momentum of a charmonium reaches about 2-3 times its mass, the quasi-DAs already converge to the LCDAs to a decent level. These results might provide some useful guidance for the future lattice study of the quasi distributions.Comment: 32 pages, 5 Figures, 1 tabl

Robust quantum repeater with atomic ensembles and single-photon sources

We present a quantum repeater protocol using atomic ensembles, linear optics and single-photon sources. Two local 'polarization' entangled states of atomic ensembles $u$ and $d$ are generated by absorbing a single photon emitted by an on-demand single-photon sources, based on which high-fidelity local entanglement between four ensembles can be established efficiently through Bell-state measurement. Entanglement in basic links and entanglement connection between links are carried out by the use of two-photon interference. In addition to being robust against phase fluctuations in the quantum channels, this scheme may speed up quantum communication with higher fidelity by about 2 orders of magnitude for 1280 km compared with the partial read (PR) protocol (Sangouard {\it et al.}, Phys. Rev. A {\bf77}, 062301 (2008)) which may generate entanglement most quickly among the previous schemes with the same ingredients.Comment: 5 pages 4 figure