摘要
量子参数估计中的基本理论——量子Cramér-Rao不等式指出,参数估计的方差由量子Fisher信息的倒数决定,量子Fisher信息越大,参数估计的方差就越小,估计精度也就会越高.在非相对论量子力学中,量子Fisher信息已被广泛研究,但考虑相对论效应对量子Fisher信息影响的研究相对较少.本文采用粒子态的相对论变换方法,数值计算和分析了运动参考系中单粒子态、双粒子态振幅参数θ和相位参数φ的量子Fisher信息.结果表明,在运动参考系中,无论是使用单粒子态还是双粒子态,量子Fisher信息都会降低.对于相位参数,双粒子态的量子Fisher信息比单粒子态降低得更加显著.然而,对于振幅参数,双粒子态的量子Fisher信息相对于单粒子态有所提高,该研究结果为在相对论效应的影响下提高参数估计精度提供了有价值的参考.
Abstract
In the field of quantum metrology,an important application is quantum parameter estimation.As the fundamental theory of quantum parameter estimation,quantum Cramér-Rao inequality shows that the variance of parameter estimation is determined by the inverse of quantum Fisher information.Higher quantum Fisher information corresponds to a lower variance,thereby improving the precision of parameter estimation.Quantum Fisher information has been extensively investigated in many aspects of non-relativistic quantum mechanics,including entanglement structure detection,quantum teleportation,quantum phase transition,quantum chaos,and quantum computation.However,there are few researches considering the influence of relativistic effect on quantum Fisher information,and therefore,we attempt to investigate this topic in this work.The relativistic transformation of particle states is employed,and the quantum Fisher information about amplitude parameter θ and phase parameter φ are investigated in moving reference frame.In this work,the parameters to be estimated are encoded into the spin degree of freedom,and the pure single-qubit state and the pure two-qubit state are both considered.The quantum Fisher information about θ and φ of single-qubit state and two-qubit state in moving reference frame are numerically calculated,respectively.It can be observed that the quantum Fisher information is associated with rapidity,amplitude parameter,and the ratio of the width to the particle mass σr/m.The quantum Fisher information of the estimated parameters decreases with rapidity increasing for both single-qubit state and two-qubit state.As rapidity approaches infinity,i.e.increases to the speed of light,the quantum Fisher information reaches to a constant which decreases as the ratio σr/m increases.More importantly,for the phase parameter,it is observed that the quantum Fisher information of two-qubit state reduces more significantly than that of single-qubit state.While,for the amplitude parameter,the quantum Fisher information of two-qubit state is greater than that of single-qubit state.These results are useful and valuable for improving the precision of parameter estimation under the influence of relativistic effect.φ θ
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