论文标题
量子多参数估计的不确定性和权衡
Uncertainty and Trade-offs in Quantum Multiparameter Estimation
论文作者
论文摘要
量子力学中的不确定性关系对我们同时获取有关量子系统不强调可观察到的期望值的知识的能力表达了界限。他们量化了有关系统的互补信息之间的准确性权衡。在量子多参数估计中，对于表征密度矩阵的不同参数可实现的精确性而发生这种权衡：不同估计器的可实现差异之间出现了不确定性关系。这与经典的多参数估计相反，在渐近极限中可以实现同时获得最佳精度。我们研究了量子多参数估计中已知的紧密界限随后的权衡关系。我们从cramér-rao类型界限计算出权衡曲线和表面，这些界限提供了在这种界限中编码的信息的引人入胜的图形表示，并认为在量子多参数估计中同时可实现的精度应视为测量不确定性不确定性关系。从参数估计中的预期成本的状态依赖性界限，我们得出了量子系统参数之间的状态独立不确定性关系。
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 quantum multiparameter estimation should be regarded as measurement uncertainty relations. From the state-dependent bounds on the expected cost in parameter estimation, we derive a state independent uncertainty relation between the parameters of a qubit system.
