论文标题
Glauber-Sudarshan $ p $ - 功能正规化的过滤功能
Filter functions for the Glauber-Sudarshan $P$-function regularization
论文作者
论文摘要
用于代表量子状态的相位空间准概率分布形式主义为量子光学的各种应用提供了实用工具，例如识别量子状态的非经典性。我们研究了为了使Glauber-Sudarshan $ P $函数正常化的过滤功能。我们表明，与滤波器函数相关的量子图是完全正面的，并且仅当此函数的傅立叶变换是概率密度分布时，因此可以在物理上实现。我们还在物理量子过滤图的输入状态和输出状态之间的保真度中得出了一个下限。因此，基于这些结果，我们证明，通过常规的Glauber-Sudarshan $ P $函数，可以通过量子状态近似任何量子状态，以进行任意准确性。我们提出了结果的应用，以估计未知量子过程的输出状态并估算量子测量的结果概率。
The phase-space quasi-probability distribution formalism for representing quantum states provides practical tools for various applications in quantum optics such as identifying the nonclassicality of quantum states. We study filter functions that are introduced to regularize the Glauber-Sudarshan $P$ function. We show that the quantum map associated with a filter function is completely positive and trace preserving and hence physically realizable if and only if the Fourier transform of this function is a probability density distribution. We also derive a lower bound on the fidelity between the input and output states of a physical quantum filtering map. Therefore, based on these results, we show that any quantum state can be approximated, to arbitrary accuracy, by a quantum state with a regular Glauber-Sudarshan $P$ function. We propose applications of our results for estimating the output state of an unknown quantum process and estimating the outcome probabilities of quantum measurements.
