Exponential Closing of the Liouvillian Gap and Persistent Conditional Correlations in Finite Open Quantum Systems

We investigate the emergence of long-lived correlations in finite open quantum systems subject to collective dissipation. By analyzing the spectral properties of the Liouvillian superoperator for systems of up to N = 6 qubits, we observe exponential suppression of the spectral gap with system size: ∆(N) ∝ e−αN with α = 1.63 ± 0.05 and coefficient of determination R2 = 0.95. This behavior implies an exponential growth of relaxation times τ = 1/∆ and signals the onset of a dissipative phase transition in the thermodynamic limit. Complementary evidence is provided by data collapse under λ/N scaling, demonstrating collective superradiant behavior, and by the saturation of conditional mutual information, indicating the persistence of nonlocal correlations. Together, these results support a mechanism of symmetry-protected information confinement in driven-dissipative quantum systems