Conditional quantum thermometry -- enhancing precision by measuring less

Abstract: Taking accurate measurements of the temperature of quantum systems is a challenging task. The mathematical peculiarities of quantum information make it virtually impossible to measure with infinite precision. In the present paper, we introduce a generalize thermal state, which is conditioned on the pointer states of the available measurement apparatus. We show that this conditional thermal state outperforms the Gibbs state in quantum thermometry. The origin for the enhanced precision can be sought in its asymmetry quantified by the Wigner-Yanase-Dyson skew information. This additional resource is further clarified in a fully resource-theoretic analysis, and we show that there is a Gibbs-preserving map to convert a target state into the conditional thermal state. We relate the quantum J-divergence between the conditional thermal state and the same target state to quantum heat.