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

中文翻译：

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热化谐振子的脉冲特征函数测量

我们提出了一种直接测量热化谐振子的 Wigner 特征函数的方法，该方法完全无法控制或测量。该策略采用了最近提出的基于探针测量的方案 [ Phys. 牧师莱特。 122 , 110406 (2019)]，它依赖于两级探头的脉冲控制。我们将此方案推广到目标谐振子的非幺正时间演化的情况，通过与有限温度环境的接触来描述其热化，以 Lindblad 主方程的形式给出。这种概括是使用超算子形式主义实现的，并为特征函数的直接测量产生分析表达式，说明测量过程中的退相干。