The description of quantum states by probability distributions of classical-like random variables associated with observables is presented. An invertible map of the wave functions and density matrices onto the probability distributions is constructed. The relation of the probability distributions to quasidistributions like the Wigner function is discussed. The interference phenomenon and superposition principle of pure quantum states are given in the form of nonlinear addition of the probabilities identified with the quantum states. The probability given by Born’s rule is expressed as a function of the probabilities describing the system states. The suggested probability representation of quantum mechanics is presented using examples of harmonic oscillators and qubits.

中文翻译：

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量子力学概率表示中的可观测量、干涉现象和玻恩定律

提出了通过与可观察量相关的经典随机变量的概率分布来描述量子态。构造了波函数和密度矩阵在概率分布上的可逆映射。讨论了概率分布与 Wigner 函数等准分布的关系。纯量子态的干涉现象和叠加原理以量子态所识别的概率的非线性相加的形式给出。Born 规则给出的概率表示为描述系统状态的概率的函数。使用谐波振荡器和量子比特的例子提出了建议的量子力学概率表示。