  This study explores the intricate real-time dynamics of a non-Hermitian
system composed of two interconnected Sachdev-Ye-Kitaev (SYK) models. A central
finding reveals that an excitation initially localized in the right SYK
subsystem can be efficiently transmitted to the left subsystem subsequent to
the characteristic scrambling time, a phenomenon facilitated by the intrinsic
non-Hermitian nature of the system. The defining hallmark of non-Hermiticity is
manifest in the asymmetric conveyance of quantum states, with the non-Hermitian
parameter functioning as a tunable knob that selectively amplifies or dampens
propagation modes on either side. Despite this inherent directional bias in
state transfer, the system sustains two distinct phases, analogously likened to
black holes and wormholes.
