Real-valued gain enabled higher-order exceptional point under anti-parity-time symmetry

Non-Hermitian systems exhibit dramatically enhanced spectral sensitivity to perturbations near higher-order exceptional points (HOEPs), with response strength scaling exponentially with the order of the exceptional point (EP). While forming such HOEPs traditionally requires hyper-dimensional parameter tuning, we theoretically demonstrate that real-valued gain can effectively substitute conventional nonlinear gain in reducing the dimensionality of HOEP formation. Specifically, under an anti-parity-time symmetric framework, we achieve coalescence of a single-EP2 and two paired-EP2s to form EP4 within only a three-dimensional parameter space. Experimentally implemented in a wireless sensing circuit with triple inductively coupled resonators, the frequency shift response to loss perturbations follows the predicted fourth-root dependence, as measured through zero-crossing analysis of the input impedance's imaginary part using impedance analyzer characterization. Notably, we observe convergent Petermann factors near this HOEP, signifying suppressed noise amplification despite eigenstate coalescence. This study establishes a dimensionality-reduction paradigm for engineering high-order non-Hermitian singularities with practical implications for ultrasensitive sensors and noise-resilient photonic/electronic systems.