Biorthogonal universal quantum control

arXiv:2610.41195v1 Announce Type: new Abstract: As a paradigm for describing open-quantum-system dynamics, the non-Hermitian Schr\"odinger equation generally modifies state norms, complicating coherent control over the system's Hilbert space. With a general instantaneous frame spanned by biorthogonal ancillary bases, we develop a biorthogonal quantum-control theory for discrete-variable systems governed by time-dependent non-Hermitian Hamiltonian. In particular, we derive a necessary and sufficient condition for extracting the transitionless pathways that transport parallel in ket and bra states.