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

Stability Analysis of Steel Lining at Pressure Diversion Tunnel Collapse Zone during Operating Period

At the collapse zone, the effects of the thickness of the consolidation grouting layer and the water pressure on the steel lining are vital to the stability of steel-lined pressure diversion tunnels. In this paper, a joint element and the load-sharing ratio of the consolidation layer are introduced to investigate the joint load-bearing characteristics of the steel lining and the consolidation layer and to determine a suitable consolidation layer thickness; a coupling method for simulating the hydromechanical interaction of the reinforced concrete lining is adopted to investigate the effect of internal water exosmosis on the seepage field at the collapse zone and to determine the external water pressure on the steel lining. In the case of a steel-lined pressure diversion tunnel, a numerical simulation is implemented to analyse the effect of the thickness of the consolidation layer and the distribution of the seepage field under the influence of internal water exosmosis. The results show that a 10 m thick consolidation layer and the adopted antiseepage measures ensure the stability of the steel lining at the collapse zone under internal and external water pressure. These research results provide a reference for the design of treatment measures for large-scale collapses in steel-lined pressure tunnels