Pulsed characteristic-function measurement of a thermalizing harmonic oscillator

We present a method for the direct measurement of Wigner characteristic function thermalizing harmonic oscillator that is completely inaccessible control or measurement. The strategy employs recently proposed probe-measurement-based scheme [Phys. Rev. Lett. 122, 110406 (2019)] which relies on pulsed two-level probe. generalize this to case nonunitary time evolution target oscillator, describing its thermalization through contact finite-temperature environment, given in form Lindblad master equation. This generalization achieved using superoperator formalism and yields analytical expressions function, accounting decoherence during process.