Quantum Parameter Estimation With Graph States In SU(N) Dynamics

In quantum metrology, achieving optimal simultaneous multiparameter estimation is of great significance but remains highly challenging. The research approach involving evolution on SU(N) dynamics provides a framework to investigate simultaneous multiparameter estimation within graph states. For single-parameter estimation, it is observed that the precision limit exceeds the Heisenberg limit in higher-dimensional SU(2) spin systems. For multiparameter estimation, two scenarios are considered: one with commutative Hamiltonian operators and another with non-commutative Hamiltonian operators. The results demonstrate that the global estimation precision exceeds the local estimation precision. Under the conditions of parameter limit, the precision of parameter estimation for simultaneously estimating each parameter is equal to that of single-parameter estimation. Furthermore, a precision-enhancement scheme has been identified that depends on the dynamics of SU(N). The smaller the value of N in the dynamic evolution, the higher the precision of the parameter estimation. Finally, it is demonstrated that graph states serve as optimal states in quantum metrology. A set of optimal measurement bases is also identified, and it is illustrated that the precision limit of multiparameter estimation can attain the quantum Cramer-Rao bound.