| （英） |
We study the estimation of the momentum shift of a relativistic spin-1/2 particle described by a gaussian wave function with a down spin in a rest frame. We then consider a situation where an observer moves along the z-axis with respect to the rest frame. We analyze the symmetric logarithmic derivative (SLD) and the lambda logarithmic derivative (lambda LD) Cramer-Rao (CR) bounds for the mean square error of estimating unitary shifts in the position by the moving observer. By a relativistic effect, the state of the moving observer after the Lorentz transformation is described by an application of the Wigner rotation, which entangles the wave function and the spin of the particle. It is shown that the trade-off relation between the mean square errors can be detected by using both the SLD and lambda LD Fisher CR bounds when the moving observer cannot measure the spin degree of freedom. |