用概率分布函数表示不可约李苏(2)代数

IF 0.7 4区物理与天体物理 Q4 OPTICS

Journal of Russian Laser Research Pub Date : 2025-02-12 DOI:10.1007/s10946-024-10228-z

Olga V. Man’ko

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引用次数: 0

摘要

利用二分类随机变量的条件概率分布描述自旋1/2态（量子比特态），利用概率分布函数构造不可约的李苏(2)代数表示。我们得到了李代数元素的显式2×2-matrices，并用泡利矩阵表示它们。然后讨论了利用量子系统态的对称李群获得任意李代数的概率表示的可能性。最后，我们用二分类随机变量的概率表示写出泡利矩阵。

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Irreducible Lie su(2) algebra representations in terms of probability distribution functions

Using spin-1/2 state (qubit state) description by the conditional probability distributions of dichotomic random variables, we construct the irreducible Lie su(2) algebra representations by means of the probability distribution functions. We obtain explicit 2×2-matrices of the Lie algebra elements and express them in terms of Pauli matrices. Then we discuss the possibility to obtain the probability representation of arbitrary Lie algebra, using the symmetry Lie group of quantum system states. Finally, we write Pauli matrices in the probability representation of dichotomic random variables.

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来源期刊

Journal of Russian Laser Research 物理-光学

CiteScore

1.50

自引率

22.20%

发文量

审稿时长

2 months

期刊介绍： The journal publishes original, high-quality articles that follow new developments in all areas of laser research, including: laser physics; laser interaction with matter; properties of laser beams; laser thermonuclear fusion; laser chemistry; quantum and nonlinear optics; optoelectronics; solid state, gas, liquid, chemical, and semiconductor lasers.