Exceptional points and quantum dynamics in a non-Hermitian two-qubit system

We study the exceptional-point (EP) structure and the associated quantum dynamics in a system consisting of a non-Hermitian qubit and a Hermitian qubit. We find that the system possesses two sets of EPs, which divide the system-parameter space into $\mathcal{P}\mathcal{T}$-symmetry unbroken, partially broken and fully broken regimes, each with distinct quantum-dynamics characteristics. Particularly, in the partially broken regime, while the $\mathcal{P}\mathcal{T}$-symmetry is generally broken in the whole four-dimensional Hilbert space, it is preserved in a two-dimensional subspace such that the quantum dynamics in the subspace are similar to those in the $\mathcal{P}\mathcal{T}$-symmetry unbroken regime. In addition, we reveal that the competition between the inter-qubit coupling and the intra-qubit driving gives rise to a complex pattern in the EP variation with system parameters.