ESTIMATION OF PURITY FOR A QUANTUM HARMONIC OSCILLATOR INITIALLY PREPARED IN A DISPLACED THERMAL STATE

We address the estimation of purity for a quantum oscillator initially prepared in a displaced thermal state and probed by a suitably prepared qubit interacting with the oscillator via Jaynes-Cummings Hamiltonian without the rotating-wave approximation. We evaluate the quantum Fisher information (QFI) and show that optimal estimation of purity can be achieved by measuring the population of the qubit after a properly chosen interaction time. We also address the estimation of purity at fixed total energy and show that the corresponding precision is independent of the presence of a coherent amplitude.