We investigate the performance of entangled coherent state for quantum enhanced phase estimation. An exact analytical expression of quantum Fisher information is derived to show the role of photon losses on the ultimate phase sensitivity. We find a transition of the sensitivity from the Heisenberg scaling to the classical scaling due to quantum decoherence of the photon state. This quantum-classical transition is uniquely determined by the number of photons being lost, instead of the number of incident photons or the photon loss rate alone. Our results also reveal that a crossover of the sensitivity between the entangled coherent state and the NOON state can occur even for very small photon loss rate.

Abstract. For typical initial and boundary conditions, a group of general solutions for the generation and dissipation of excess pore water pressure in stone column composite foundation under coupling action of dynamic and static loads have been developed by separation of variables and Green functions to the control differential equations. In the control equation, the pore pressure increasing ratio is expressed as the function of depth and time. A special solution is obtained to zero initial condition and upper boundary pervious, based on an existing dynamic pore pressure calculation model. The numerical example shows that the effect of seepage of the stone column is prominent.