The information theoretic concepts are crucial to study the quantum mechanical systems. In this paper, the information densities of 𝒫𝒯-symmetric potential have been demonstrated and their properties deeply analyzed. The position space and momentum space information entropy is obtained and Bialynicki-Birula–Mycielski inequality is saturated for different parameters of the potential. Some interesting features of information entropy have been discussed. The variation in these entropies is described which gets saturated for specific values of the parameter. These have also been analyzed for the 𝒫𝒯-symmetry breaking case. Further, the entropy squeezing phenomenon has been investigated in position space as well as momentum space. Interestingly, 𝒫𝒯 phase transition conjectures the entropy squeezing in position space and momentum space.

中文翻译：

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𝒫𝒯-对称势的量子信息熵和压缩

信息论概念对于研究量子力学系统至关重要。在本文中，信息密度𝒫𝒯-对称势已被证明并深入分析了它们的性质。获得了位置空间和动量空间信息熵，并且 Bialynicki-Birula-Mycielski 不等式对于势的不同参数是饱和的。已经讨论了信息熵的一些有趣特征。这些熵的变化被描述为对于参数的特定值变得饱和。这些也被分析为𝒫𝒯-对称破案。此外，熵压缩现象已经在位置空间和动量空间中进行了研究。有趣的是，𝒫𝒯相变推测位置空间和动量空间中的熵压缩。