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We apply estimation theory to a system formed by two interacting trappedions. By using the Fisher matrix formalism, we introduce a simple scheme forestimation of the temperature of the longitudinal vibrational modes of theions. We use the ions interaction to effectively infer the temperature of theindividual ions, by optimising the interaction time evolution and by measuringonly over one of the ions. We also investigate the effect of a non-thermalreservoir over the inference approach. The non-classicality of one of the ionsvibrational modes, introduced due to a squeezed thermal reservoir, improves theindirect inference of the individual temperatures.

Temperature estimation of an entangled pair of trapped ions