Directional Dynamics of the Non-Hermitian Skin Effect

The dynamical consequences of the non-Hermitian skin effect (NHSE) remain largely unexplored despite extensive studies of its static properties. Here we address this gap by applying quantum Liang information flow (QLIF) an inherently directional measure of causal influence to the nonHermitian Su Schrieffer Heeger model with non reciprocal hopping. Unlike symmetric correlation functions, QLIF directly captures the directional asymmetry characteristic of non reciprocal systems. We demonstrate a scissors effect where the asymmetry varies approximately linearly with the non-reciprocity parameter gamma for small gamma, and exhibits non-monotonic dependence on the skin length, with optimal asymmetry at moderate skin localization. The velocity ordering reveals NHSE-induced blocking of information flow against the skin direction. Three distinct temporal regimes emerge: light-cone-bounded spreading, gamma-dependent stabilization, and coherent oscillations. These results establish the first quantitative connection between static skin localization and directional information dynamics, offering new insights into information propagation in non-reciprocal quantum systems.