Role of inefficient measurement in realizing post-selection-based non-Hermitian qubits

• URL: http://arxiv.org/abs/2510.21159v1
• Date: Fri, 24 Oct 2025 05:16:40 GMT
• Title: Role of inefficient measurement in realizing post-selection-based non-Hermitian qubits
• Authors: Roson Nongthombam, Aman Verma, Amarendra K. Sarma,
• Abstract summary: We introduce post-selection efficiencies for both decay channels, the second-excited to first-excited and the first-excited to ground-state transitions.<n>We find that the decoherence effects arising from quantum jumps within the second-excited and first-excited manifold also manifest under inefficient post-selection of the second-excited to first-excited transitions.
• Score: 1.0323063834827415
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Post-selecting against quantum jumps into the ground state confines the evolution of the three-level system to the excited states manifold, effectively realizing a PT-symmetric non-Hermitian qubit. In this work, by introducing post-selection efficiencies for both decay channels, the second-excited to first-excited and the first-excited to ground-state transitions, we formulate a hybrid-Liouvillian framework that captures the unmonitored dynamics of the non-Hermitian qubit. We find that the decoherence effects arising from quantum jumps within the second-excited and first-excited manifold also manifest under inefficient post-selection of the second-excited to first-excited transitions, thereby modifying the spectral properties of the Liouvillian and leading to a splitting of the exceptional points. A comparative analysis shows that the trajectory-based approach, obtained by ensemble-averaging stochastic measurement trajectories generated via the Bayesian state update rule, and the Lindblad evolution remain consistent. Our results highlight the fundamental role of measurement inefficiency in realizing post-selection-based non-Hermitian qubits and in shaping the structure of Liouvillian exceptional points. These findings provide new insights into how inefficient measurement processes influence non-Hermitian behavior in open quantum systems.

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