Role of inefficient measurement in realizing post-selection-based non-Hermitian qubits
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| Format: | Preprint |
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2025
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| author | Nongthombam, Roson Verma, Aman Sarma, Amarendra K. |
| author_facet | Nongthombam, Roson Verma, Aman Sarma, Amarendra K. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_21159 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Role of inefficient measurement in realizing post-selection-based non-Hermitian qubits Nongthombam, Roson Verma, Aman Sarma, Amarendra K. Quantum Physics 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. |
| title | Role of inefficient measurement in realizing post-selection-based non-Hermitian qubits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.21159 |