Symmetry-Enforced Non-Hermitian Jarzynski Equality in an SU(2)-Rotated Family of Hybrid PT−APT Systems

The Jarzynski equality is a cornerstone of nonequilibrium thermodynamics, linking work statistics to equilibrium freeenergy differences. Although it has been extensively verified in classical and quantum Hermitian settings, its status in non-Hermitian dynamics remains under debate. Here we show that, in a post-selected no-quantum-jump framework, a conditional non-Hermitian Jarzynski equality holds when the transition probabilities obey a parity-exchange symmetry. We study a constructed family of two-level hybrid Hamiltonians formed as linear combinations of parity-time (PT) and anti-parity-time (APT) symmetric terms, and demonstrate using complementary geometric and algebraic arguments that the parity-exchange symmetry persists throughout the corresponding SU(2)-rotated orbit. Relative to previous PT-focused conditional Jarzynski equality results, the advance here is an extension of the symmetry criterion from the isolated PT endpoint to a broader PT−APT hybrid family. Experimentally, we implement three representative points, θk = 0, π/4, π/2, in a single trapped 171Yb+ ion and measure the resulting work distributions under cyclic protocols with ΔF = 0, confirming the predicted symmetry criterion at those points. Our results establish a symmetry-based extension of the conditional non-Hermitian Jarzynski relation within this restricted two-level setting.