  Open systems with gain and loss, described by non-trace-preserving,
non-Hermitian Hamiltonians, have been a subject of intense research recently.
The effect of exceptional-point degeneracies on the dynamics of classical
systems has been observed through remarkable phenomena such as the parity-time
symmetry breaking transition, asymmetric mode switching, and optimal energy
transfer. On the other hand, consequences of an exceptional point for quantum
evolution and decoherence are hitherto unexplored. Here, we use post-selection
on a three-level superconducting transmon circuit with tunable Rabi drive,
dissipation, and detuning to carry out quantum state tomography of a single
dissipative qubit in the vicinity of its exceptional point. Quantum state
tomography reveals the PT symmetry breaking transition at zero detuning,
decoherence enhancement at finite detuning, and a quantum signature of the
exceptional point in the qubit relaxation state. Our observations demonstrate
rich phenomena associated with non-Hermitian physics such as non-orthogonality
of eigenstates in a fully quantum regime and open routes to explore and harness
exceptional point degeneracies for enhanced sensing and quantum information
processing.
