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Quasi-probability distributions in Loop Quantum Cosmology
Classical and Quantum Gravity ( IF 3.5 ) Pub Date : 2020-10-07 , DOI: 10.1088/1361-6382/abb57a
Jasel Berra-Montiel 1, 2 , Alberto Molgado 1, 2
Affiliation  

In this paper, we introduce a complete family of parametrized quasi-probability distributions in phase space and their corresponding Weyl quantization maps with the aim to generalize the recently developed Wigner-Weyl formalism within the Loop Quantum Cosmology program (LQC). In particular, we intend to define those quasi-distributions for states valued on the Bohr compactification of the real line in such a way that they are labeled by a parameter that accounts for the ordering ambiguity corresponding to non-commutative quantum operators. Hence, we notice that the projections of the parametrized quasi-probability distributions result in marginal probability densities which are invariant under any ordering prescription. We also note that, in opposition to the standard Schrodinger representation, for an arbitrary character the quasi-distributions determine a positive function independently of the ordering. Further, by judiciously implementing a parametric-ordered Weyl quantization map for LQG, we are able to recover in a simple manner the relevant cases of the standard, anti-standard, and Weyl symmetric orderings, respectively. We expect that our results may serve to analyze several fundamental aspects within the LQC program, in special those related to coherence, squeezed states, and the convergence of operators, as extensively analyzed in the quantum optics and in the quantum information frameworks.

中文翻译:

圈量子宇宙学中的准概率分布

在本文中,我们介绍了一系列完整的相空间参数化准概率分布及其相应的 Weyl 量化图,目的是在循环量子宇宙学程序 (LQC) 中推广最近开发的 Wigner-Weyl 形式主义。特别是,我们打算定义那些在实线的玻尔紧化上取值的状态的准分布,以这样一种方式,它们由一个参数标记,该参数说明对应于非交换量子算子的排序模糊性。因此,我们注意到参数化准概率分布的投影导致边际概率密度在任何排序规则下都是不变的。我们还注意到,与标准的薛定谔表示相反,对于任意字符,准分布确定独立于排序的正函数。此外,通过明智地为 LQG 实现参数有序的外尔量化映射,我们能够以简单的方式分别恢复标准、反标准和外尔对称排序的相关情况。我们希望我们的结果可以用于分析 LQC 程序中的几个基本方面,特别是与相干性、压缩态和算子收敛相关的方面,正如在量子光学和量子信息框架中广泛分析的那样。和 Weyl 对称排序,分别。我们希望我们的结果可以用于分析 LQC 程序中的几个基本方面,特别是与相干性、压缩态和算子收敛相关的方面,正如在量子光学和量子信息框架中广泛分析的那样。和 Weyl 对称排序,分别。我们希望我们的结果可以用于分析 LQC 程序中的几个基本方面,特别是与相干性、压缩态和算子收敛相关的方面,正如在量子光学和量子信息框架中广泛分析的那样。
更新日期:2020-10-07
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