Role of Inefficient Measurement in Generating Post‐Selection‐Based Non‐Hermitian Qubits

ABSTRACT

Post‐selecting against quantum jumps into the ground state confines the evolution of the three‐level system to the excited – manifold, effectively realizing a ‐symmetric non‐Hermitian qubit. In this work, by introducing post‐selection efficiencies for both decay channels, and , we formulate a hybrid‐Liouvillian framework that captures the unmonitored dynamics of this non‐Hermitian qubit. We find that the decoherence effects arising from quantum jumps within the – manifold also manifest under inefficient post‐selection of – transitions, thereby modifying the spectral properties of the Liouvillian. A comparative analysis shows that the trajectory‐based approach and the ensemble‐averaged Lindblad evolution remain consistent for drive strengths far from the EP. Near the EP, the nonlinearity introduced by the normalization due to postselection becomes significant in the dynamics, which results in a deviation between the Liouvillian evolution and the trajectory average. We show how inefficiency in the postselection relaxes this normalization and consequently reduces the deviation. Our results provide new insights into how the inefficient measurement influences non‐Hermitian dynamics in open quantum systems.