Berry curvature as a lower bound for multi-parameter estimation

讲座内容：Quantum Fisher information (QFI) is a key concept in quantumstate estimation, and Berry curvature (BC) is another basic concept to describegeometric properties of quantum states. In this report, we consider pure statesundergoing unitary parametrization processes and show that the BC serves as alower bound for the product of QFIs corresponding to two different parametersthrough the Heisenberg uncertainty relation. This relation between QFI and BCimplies that the estimation precisions of two different parameters are mutuallyrestrictive due to finite BC, and the notion of QFI squeezing is introduced. Ascenario of general su(2) parametrization is considered in detail to verify therelation between the QFI and BC.