We demonstrate that the presence of a twist phase in a random light beam leads to classical entanglement between phase space degrees of freedom of the beam. We find analytically the bi-orthogonal decomposition of the Wigner function of a twisted Gaussian Schell-model (TGSM) source and quantify its entanglement by evaluating the Schmidt number of the decomposition. We show that (i) classical entanglement of a TGSM source vanishes concurrently with the twist in the fully coherent limit and (ii) entanglement dramatically increases as the source coherence level decreases. We also show that the discovered type of classical entanglement of a Gaussian Wigner function does not degrade on beam propagation in free space.

中文翻译：

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部分相干光的扭曲相位和经典纠缠

我们证明了随机光束中扭曲相位的存在导致光束的相空间自由度之间的经典纠缠。我们分析地发现了扭曲高斯谢尔模型 (TGSM) 源的 Wigner 函数的双正交分解，并通过评估分解的施密特数来量化其纠缠。我们表明（i）TGSM 源的经典纠缠与完全相干极限中的扭曲同时消失，（ii）纠缠随着源相干水平的降低而显着增加。我们还表明，所发现的高斯维格纳函数的经典纠缠类型不会在自由空间中的光束传播中降低。