| Summary: | The precise knowledge of the temperature of an ultracold lattice gas simulating a strongly correlated system is a question of both fundamental and technological importance. Here, we address such question by combining tools from quantum metrology together with the study of the quantum correlations embedded in the system at finite temperatures. Within this frame we examine the spin- $1/2$ XY chain, first estimating, by means of the quantum Fisher information, the lowest attainable bound on the temperature precision. We then address the estimation of the temperature of the sample from the analysis of correlations using a quantum non demolishing Faraday spectroscopy method. Remarkably, our results show that the collective quantum correlations can become optimal observables to accurately estimate the temperature of our model in a given range of temperatures.
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