Transient entanglement generation in driven chiral networks beyond the secular approximation

We study transient entanglement generation between two quantum nodes coupled through a chiral one-dimensional channel. In an emitter-only Born-Markov description, we show that continuous driving and an initial ground state can raise the maximum transient concurrence above the undriven $2/e$ benchmark associated with the effectively single-excitation model. We then consider a more microscopic XX spin-chain channel with triangular plaquette couplings and compare a nonsecular time-convolutionless master equation (TCL-ME) with matrix-product-state (MPS) simulations. In the optimal driven regime, the nonsecular TCL-2 treatment reproduces the concurrence envelope and first transient peak qualitatively, while the remaining discrepancy is mainly attributable to beyond-Born system-bath correlations. The enhancement is traced to the failure of the secular approximation under strong driving, where nearby dressed transitions are not well separated on the dissipative timescale and nonsecular terms mix dressed-state coherences. Finally, we examine within TCL-2 the sensitivity of the protocol to positional disorder, imperfect chirality, and loss into nonguided modes. These results clarify when the familiar $2/e$ limitation ceases to apply and separate the roles of secular breakdown, Born-factorization error, and reduced-state memory in driven chiral entanglement generation; we believe that our study contributes to one of the first studies where the breakdown of the secular approximation is useful rather than detrimental.