Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between complementary pieces of information about the system. In quantum multiparameter estimation, such trade-offs occur for the precision achievable for different parameters characterizing a density matrix: an uncertainty relation emerges between the achievable variances of the different estimators. This is in contrast to classical multiparameter estimation, where simultaneous optimal precision is attainable in the asymptotic limit. We study trade-off relations that follow from known tight bounds in quantum multiparameter estimation. We compute trade-off curves and surfaces from Cramér–Rao type bounds which provide a compelling graphical representation of the information encoded in such bounds, and argue that bounds on simultaneously achievable precision in qua...

中文翻译：

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量子多参数估计中的不确定性和权衡

量子力学中的不确定性关系限制了我们同时获得有关量子系统非交换观测值的期望值的知识的能力。他们量化了有关系统的补充信息之间的准确性之间的权衡。在量子多参数估计中，这种折衷是针对表征密度矩阵的不同参数可达到的精度而发生的：在不同估计量可实现的方差之间会出现不确定性关系。这与经典的多参数估计相反，经典的多参数估计在渐近极限中可以同时获得最佳精度。我们研究在量子多参数估计中紧迫的已知界限之间的取舍关系。