论文标题
Wigner旋转对估计相对论旋转1/2粒子的统一转移参数的影响
Effect of Wigner rotation on estimating unitary-shift parameter of relativistic spin-1/2 particle
论文作者
论文摘要
我们获得了估计相对论粒子位置的预期值的准确性极限，以沿恒定速度沿一个方向移动的观察者。我们使用由高斯波函数描述的相对论自旋1/2粒子的特定模型，其余框架在其余框架中旋转。为了得出移动观察者粒子的状态矢量，我们使用纠缠自旋和粒子动量的Wigner旋转。基于该移动框架的此波函数，我们获得了对称对数衍生物（SLD）Cramer-Rao结合，该结合设置了任意移动观察者的估计精度极限。结果表明，当移动观察者无法测量自由度的自由度时，估计精度在观察者的速度下单调降低。这意味着估计准确性极限会随着观察者的速度增加而恶化，但即使在相对论极限下也是有限的。我们通过任意移动框架中SLD Fisher信息矩阵的精确计算来得出此信息损失的数量。
We obtain the accuracy limit for estimating the expectation value of the position of a relativistic particle for an observer moving along one direction at a constant velocity. We use a specific model of a relativistic spin-1/2 particle described by a gaussian wave function with a spin down in the rest frame. To derive the state vector of the particle for the moving observer, we use the Wigner rotation that entangles the spin and the momentum of the particle. Based on this wave function for the moving frame, we obtain the symmetric logarithmic derivative (SLD) Cramer-Rao bound that sets the estimation accuracy limit for an arbitrary moving observer. It is shown that estimation accuracy decreases monotonically in the velocity of the observer when the moving observer does not measure the spin degree of freedom. This implies that the estimation accuracy limit worsens with increasing the observer's velocity, but it is finite even in the relativistic limit. We derive the amount of this information loss by the exact calculation of the SLD Fisher information matrix in an arbitrary moving frame.
