Cost-effective estimation of single-mode thermal states by probabilistic quantum metrology

In probabilistic quantum metrology, one aims at finding measurements that concentrate the Fisher information on the resulting conditional quantum states, i.e. those states post-selected according to the outcome of the measurement. The quantum Cramer-Rao (QCR) bound itself cannot be surpassed this way, but it could be possible to improve the information-cost ratio (where cost refers to the experimental implementation), or even the total Fisher information. In this paper, we propose a post-selection protocol achieving this goal using single-photon subtraction and thermal states of radiation. In particular, we achieve a larger information-cost ratio for the estimation of temperature than the strategy attaining the QCR bound. Our scheme involves only classical states of radiation and this contrasts with (but does not contradict) recent results proving that for unitary quantum statistical models, post-selection strategies can outperform direct protocols only exploiting nonclassical states.