Temperature as an environmental parameter influences the evolution of an open quantum system. In detail, temperature lies in Lindblad operator of quantum master equation that the evolution of an open quantum system follows. Hence, one can implement a temperature estimation of thermal baths through a measurement of quantum Fisher information about temperature brought from quantum states. Such a method by calculating quantum Fisher information about a parameter to estimate its value avoids measuring the parameter directly and it does not change the value of the parameter due to making measurements. In this paper, we consider a model consisting of a XXZ spin-[Formula: see text] chain coupled locally to independent thermal baths with different temperature. Based on the model, we investigate optimal temperature estimation for thermal baths with respect to an open quantum system subjected to non-steady states. We first study optimal probe time for temperature estimation in the case of non-steady states and find that the optimal time shows different features for different types of system variables. It proves that in a certain duration there exists a tradeoff between the trial times and the attaining amount of Fisher information in each trial. In addition, we pay attention to an issue on optimal probe states. We demonstrate that in many cases the optimal states are not always the maximally entangled states and even maybe the separable states, which is related with the measuring time, system couplings.
Auxiliary open quantum system for the Floquet quantum master equation