Directional dynamics of the non-Hermitian skin effect

The dynamical consequences of the non-Hermitian skin effect (NHSE), while increasingly studied, have so far received less systematic attention than its now well-characterized static properties. Here we contribute to this developing front by applying quantum Liang information flow (QLIF)—an inherently directional measure of causal influence—to the non-Hermitian Su-Schrieffer-Heeger model with non-reciprocal hopping. Unlike symmetric correlation functions, QLIF directly captures the directional asymmetry TR→L≠TL→R characteristic of non-reciprocal systems. We demonstrate a “scissors effect” where the asymmetry ΔT varies approximately linearly with the non-reciprocity parameter γ for small |γ|, and exhibits non-monotonic dependence on the skin length ξ, with optimal asymmetry at moderate skin localization. The velocity ordering ʋeff (γ < 0) > ʋeff (0) > ʋeff (γ > 0) reveals NHSE-induced blocking of information flow against the skin direction. Three distinct temporal regimes emerge: light-cone-bounded spreading, γ-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.