Effect of Wigner rotation on estimating the unitary-shift parameter of a relativistic spin-1/2 particle
Effect of Wigner rotation on estimating the unitary-shift parameter of a relativistic spin-1/2 particle
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DOI：
10.1103/physreva.106.062404
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发表时间：
2022-04
影响因子：
2.9
通讯作者：
S. Funada;J. Suzuki
中科院分区：
文献类型：
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作者：
S. Funada;J. Suzuki
我们得到了观测者沿沿着一个方向作匀速运动时估计相对论性粒子位置期望值的精度极限。我们使用一个相对论性自旋为1 / 2的粒子的特定模型，该模型由在静止坐标系中自旋向下的高斯波函数描述。为了推导出运动观察者的粒子状态矢量，我们使用了纠缠粒子自旋和动量的维格纳旋转。基于这个波函数的运动框架，我们得到的对称对数导数（SLD）Cram 'er-Rao界，设置一个任意移动的观察器的估计精度限制。它示出的估计精度单调下降时，移动的观察员不测量自旋自由度的观察员的速度。这意味着估计精度极限随着观测者速度的增加而增加，但即使在相对论极限下也是有限的。我们推导出这种信息损失量的精确计算的SLD Fisher信息矩阵在任意移动帧。
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) Cram´er-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.