Fig. 1. Non-Hermitian Hamiltonian as a phenomenological description of open systems

Fig. 2. Non-Hermitian operator eigenstate non-orthogonality and sensitivity enhancement^[13]. (a) Nonorthogonal energy eigenstates as eigenvectors in Hilbert space; (b) energy splitting and perturbation strength for exceptional point (red solid curve) and conventional degeneracy (blue dashed curve); (c) relationship between splitting enhancement factor of exceptional point-based sensor (red solid curve) and perturbation strength, blue dashed line marks the reference value of unity

Fig. 3. Schematic of quantum parameter estimation

Fig. 4. Mechanism of the non-Hermiticity-enhanced sensing^[11]

Fig. 5. Comparison of sensors operating at exceptional point and diabolic point^[22]

Fig. 6. Brillouin control of state vectors in non-Hermitian system^[5]

Fig. 7. Brillouin laser linewidth enhancement near exceptional point^[6]

Fig. 8. Experimental schematic of the non-Hermitian cyclic quantum evolution^[11]

Fig. 9. Quantum metrology in non-Hermitian system

Fig. 10. Post-selected scheme for non-unitary evolution^[9]

Fig. 11. Experimental device of non-Hermitian evolution^[9]

Fig. 12. Experimental setup for testing the uncertainty relations between two non-Hermitian operators A and B in two scenarios^[55]