Quantum uncertainty relations constrain the precision of measurements across multiple non-commuting quantum mechanical observables.Here,we introduce the concept of optimal observable sets and define the tightest uncer...Quantum uncertainty relations constrain the precision of measurements across multiple non-commuting quantum mechanical observables.Here,we introduce the concept of optimal observable sets and define the tightest uncertainty constants to accurately describe these measurement uncertainties.For any quantum state,we establish optimal sets of three observables for both product and summation forms of uncertainty relations,and analytically derive the corresponding tightest uncertainty constants.We demonstrate that the optimality of these sets remains consistent regardless of the uncertainty relation form.Furthermore,the existence of the tightest constants excludes the validity of standard real quantum mechanics,underscoring the essential role of complex numbers in this field.Additionally,our findings resolve the conjecture posed in[Phys.Rev.Lett.118,180402(2017)],offering novel insights and potential applications in understanding preparation uncertainties.展开更多
Quite many authors have dealt with the estimation of the parameters of normal distribution on the basis of non-homogeneous sets: Hald A. 1949 [1], Arango-Castillo L. and Takahara G. 2018 [2]. All the robust methods ar...Quite many authors have dealt with the estimation of the parameters of normal distribution on the basis of non-homogeneous sets: Hald A. 1949 [1], Arango-Castillo L. and Takahara G. 2018 [2]. All the robust methods are based on the assumption that the results affected by gross errors can be found to the left and/or to the right of censoring, or truncated, points. However, as a rule, the (intrinsic) distribution of observations is complex (mixed) consisting of two or more distributions. Then the existing methods, such as ML, Huber’s, etc., yield enlarged estimates for the normal-distribution variance. By studying better estimates the present author has invented new method, called PEROBLS D, based on the Tukeyan mixed-distribution model in which both the contamination rate (percentage) and the parameters of both distributions, forming the mixed one, are estimated, and for the parameters of the basic normal distribution better estimates are obtained than by the existing methods.展开更多
基金supported by the National Natural Science Foundation of China(NSFC)(Grant Nos.12065021,12075159,12171044,and 12175147)。
文摘Quantum uncertainty relations constrain the precision of measurements across multiple non-commuting quantum mechanical observables.Here,we introduce the concept of optimal observable sets and define the tightest uncertainty constants to accurately describe these measurement uncertainties.For any quantum state,we establish optimal sets of three observables for both product and summation forms of uncertainty relations,and analytically derive the corresponding tightest uncertainty constants.We demonstrate that the optimality of these sets remains consistent regardless of the uncertainty relation form.Furthermore,the existence of the tightest constants excludes the validity of standard real quantum mechanics,underscoring the essential role of complex numbers in this field.Additionally,our findings resolve the conjecture posed in[Phys.Rev.Lett.118,180402(2017)],offering novel insights and potential applications in understanding preparation uncertainties.
文摘Quite many authors have dealt with the estimation of the parameters of normal distribution on the basis of non-homogeneous sets: Hald A. 1949 [1], Arango-Castillo L. and Takahara G. 2018 [2]. All the robust methods are based on the assumption that the results affected by gross errors can be found to the left and/or to the right of censoring, or truncated, points. However, as a rule, the (intrinsic) distribution of observations is complex (mixed) consisting of two or more distributions. Then the existing methods, such as ML, Huber’s, etc., yield enlarged estimates for the normal-distribution variance. By studying better estimates the present author has invented new method, called PEROBLS D, based on the Tukeyan mixed-distribution model in which both the contamination rate (percentage) and the parameters of both distributions, forming the mixed one, are estimated, and for the parameters of the basic normal distribution better estimates are obtained than by the existing methods.
