Institute of Applied Physics and Materials Engineering, University of Macau, Macau S.A.R, China.
Sci Rep. 2022 Dec 7;12(1):21157. doi: 10.1038/s41598-022-25796-w.
When considered as orthogonal bases in distinct vector spaces, the unit vectors of polarization directions and the Laguerre-Gaussian modes of polarization amplitude are inseparable, constituting a so-called classical entangled light beam. Equating this classical entanglement to quantum entanglement necessary for computing purpose, we show that the parallelism featured in Shor's factoring algorithm is equivalent to the concurrent light-path propagation of an entangled beam or pulse train. A gedanken experiment is proposed for executing the key algorithmic steps of modular exponentiation and Fourier transform on a target integer N using only classical manipulations on the amplitudes and polarization directions. The multiplicative order associated with the sought-after integer factors is identified through a four-hole diffraction interference from sources obtained from the entangled beam profile. The unique mapping from the fringe patterns to the computed order is demonstrated through simulations for the case [Formula: see text].
当在不同的向量空间中被视为正交基时，偏振方向的单位向量和偏振幅度的拉盖尔-高斯模式是不可分离的，构成了所谓的经典纠缠光束。将这种经典纠缠等同于计算所需的量子纠缠，我们表明 Shor 因式分解算法中的并行性等效于纠缠光束或脉冲串的并发光路传播。提出了一个思维实验，用于仅通过对幅度和偏振方向进行经典操作，在目标整数 N 上执行模幂运算和傅里叶变换的关键算法步骤。通过从纠缠光束轮廓获得的源的四孔衍射干涉，确定与所寻求的整数因子相关的乘法阶。通过模拟[公式：见文本]的情况，演示了从条纹图案到计算阶的唯一映射。
