A Hermitian bypass to the non-Hermitian quantum theory

Abstract Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to singularities (e.g. exceptional points and decoherence) arising from interactions with the environment. Here, we introduce a well-defined reference or computational basis for representing the NH Hamiltonian eigenstates, where singularities are shifted from the basis states to the expansion coefficients. This approach simplifies the mathematical treatment of open quantum systems. Furthermore, we propose a local ‘space-time’ transformation on the computational basis that defines a generic dual space mapping. Interestingly, this transformation reveals a static/global symmetry for real/imaginary energy values, unveiling inherent conserved quantities in open quantum systems. Our formalism provides new insights into key features such as exceptional points, dual space maps, and the origin of symmetry-enforced real eigenvalues. The framework is broadly applicable across various areas of physics where NH operators appear as ladder operators, order parameters, self-energies, projectors, and other entities.