Multiparameter estimation of quantum metrology in a Heisenberg system with Dzyaloshinskii-Moriya interaction

In this work, we study the quantum Fisher information on the Heisenberg model in presence of the Dzyaloshinskii-Moriya interaction, basing on the multi-parametric estimation strategy in quantum metrology. First, we employ the density matrix vectorization method with a tool of the quantum Fisher information matrix through quantum Cramer-Rao bound. Second, we show that the multi-parameter quantum Cramer-Rao bound for simultaneous and individual estimation of the temperature and Dzyaloshinskii-Moriya interaction strongly relies on the concepts of the quantum Fisher information matrix. We confirm also the simultaneous strategy that provides a high precision than the individual.