Cost-effective temperature estimation strategies for thermal states with probabilistic quantum metrology
arXiv:2111.05285 · doi:10.1088/2058-9565/ac6dfe
Abstract
In probabilistic quantum metrology, one aims at finding weak measurements that concentrate the Fisher Information on the resulting quantum states, post-selected according to the weak outcomes. Though the Quantum Cramér-Rao bound itself cannot be overshot this way, it could be possible to improve the information-cost ratio, or even the total Fisher Information. We propose a post-selection protocol achieving this goal based on single-photon subtraction onto a thermal state of radiation yielding a greater information-cost ratio for the temperature parameter with respect to the standard strategy required to achieve the Quantum Cramér-Rao bound. We address just fully-classical states of radiation: this contrasts with (but does not contradict) a recent result proving that, concerning unitary quantum estimation problems, post-selection strategies can outperform direct measurement protocols only if a particular quasiprobability associated with the family of parameter-dependent quantum states becomes negative, a clear signature of nonclassicality.
20 pages; comments are welcome
References in corpus (8)
- Increasing entanglement between Gaussian states by coherent photon subtraction
- Global Quantum Thermometry
- Precision measurements with photon-subtracted or photon-added Gaussian states
- Quantum Metrology: Extended Convexity of Quantum Fisher Information
- Thermometry of Gaussian quantum systems using Gaussian measurements
- Optimal probabilistic estimation of quantum states
- Probabilistic metrology or how some measurement outcomes render ultra-precise estimates
- Introduction to generation, manipulation and characterization of optical quantum states