Liouvillian versus Hamiltonian Exceptional Points as Stationary Sensing Resources: a Two-Level Dissipative Case Study

H.-Y. Liu

Published Oct 28, 2026• 0 citations

Abstract

Abstract Exceptional points (EPs) of the effective non-Hermitian Hamiltonian and of the Liou- villian superoperator are often treated interchangeably in dissipative quantum sensing. In the exactly solvable amplitude-damped two-level sensor we prove that the two degeneracies live at different parameter points—the Hamiltonian EP at (ε,∆) = (0,γ/2), where the Li- ouvillian spectrum is perfectly regular, and the genuine Liouvillian EP at (0,γ/4), where a Jordan block appears—and derive the closed-form stationary quantum Fisher informa- tion (QFI), finite at both EPs and globally maximized at a non-EP point. The divergent response motivating EP sensing lives exclusively in the no-jump (post-selected) sector, at a post-selection success cost that vanishes linearly with the detuning. We classify Liouvil- lian EPs into gap-closing (type I, genuine critical resources) and finite-rate (type II, not resources), validated by a degenerate parametric oscillator, and benchmark the stationary results against the scattering-matrix QFI bound of Wiersig and Rotter (enhancement factor 4 reproduced). Forstationarydissipativesensors, neitherEPalonegrantsQFIenhancement.

DOI: 10.21203/rs.3.rs-11520823/v1

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