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

Abstract

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.