Sanz Ángel S
Department of Optics, Faculty of Physical Sciences, Universidad Complutense de Madrid, Pza. Ciencias 1, Ciudad Universitaria, 28040 Madrid, Spain.
Entropy (Basel). 2023 Jul 17;25(7):1077. doi: 10.3390/e25071077.
We consider the concept of velocity fields, taken from Bohmian mechanics, to investigate the dynamical effects of entanglement in bipartite realizations of Young's two-slit experiment. In particular, by comparing the behavior exhibited by factorizable two-slit states (cat-type state analogs in the position representation) with the dynamics exhibited by a continuous-variable Bell-type maximally entangled state, we find that, while the velocity fields associated with each particle in the separable scenario are well-defined and act separately on each subspace, in the entangled case there is a strong deformation in the total space that prevents this behavior. Consequently, the trajectories for each subsystem are not constrained any longer to remain confined within the corresponding subspace; rather, they exhibit seemingly wandering behavior across the total space. In this way, within the subspace associated with each particle (that is, when we trace over the other subsystem), not only interference features are washed out, but also the so-called Bohmian non-crossing rule (i.e., particle trajectories are allowed to get across the same point at the same time).
我们采用源于玻姆力学的速度场概念，来研究杨氏双缝实验二分实现中纠缠的动力学效应。具体而言，通过比较可因式分解的双缝态（位置表象中的类猫态类似物）所展现的行为与连续变量贝尔型最大纠缠态所呈现的动力学，我们发现，在可分情形中与每个粒子相关联的速度场是明确界定的，且分别作用于每个子空间，但在纠缠情形下，全空间中存在强烈变形，阻止了这种行为。因此，每个子系统的轨迹不再局限于相应子空间内；相反，它们在全空间中呈现出看似漫游的行为。这样一来，在与每个粒子相关联的子空间内（即当我们对另一个子系统求迹时），不仅干涉特征被消除，而且所谓的玻姆非交叉规则（即粒子轨迹被允许在同一时间穿过同一点）也不再成立。
