Improved quantum entropic uncertainty relations

We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and the tighter state-dependent one based on the majorization techniques. The analytical results for qubit and qutrit systems with two or three measurement settings are explicitly derived, with detailed examples showing that they outperform the existing bounds. The case with the presence of quantum memory is also investigated.Comment: 14 pages,6 figure

Multi Weyl Points and the Sign Change of Their Topological Charges in Woodpile Photonic Crystals

We show that Weyl points with topological charges 1 and 2 can be found in very simple chiral woodpile photonic crystals, which can be fabricated using current techniques down to the nano-scale. The sign of the topological charges can be tuned by changing the material parameters of the crystal, keeping the structure and the symmetry unchanged. The underlying physics can be understood using a tight binding model, which shows that the sign of the charge depends on the hopping range. Gapless surface states and their back-scattering immune properties are also demonstrated in these systems

Electronic transport of bilayer graphene with asymmetry line defects

In this paper, we study the quantum properties of a bilayer graphene with (asymmetry) line defects. The localized states are found around the line defects. Thus, the line defects on one certain layer of the bilayer graphene can lead to an electric transport channel. By adding a bias potential along the direction of the line defects, we calculate the electric conductivity of bilayer graphene with line defects using Landauer-B\"{u}ttiker theory, and show that the channel affects the electric conductivity remarkably by comparing the results with those in a perfect bilayer graphene. This one-dimensional line electric channel has the potential to be applied in the nanotechnology engineering.Comment: 5 pages, 7 figure