A three-layer diagnostic framework integrating spectral decomposition, entanglement topology analysis, and quantum synchronization witnesses for characterizing genuinely quantum collective phenomena in Lindblad-governed open quantum networks.
Open quantum networks governed by Lindblad master equations exhibit non-classical emergent behaviors beyond consensus that lack systematic diagnostic tools. This work addresses the gap identified by Wen et al. (2026) by providing a unified, computationally tractable framework to diagnose, classify, and predict non-classical collective phenomena across arbitrary network topologies.
Full eigenspectrum analysis of the Lindbladian superoperator in Liouville space. Identifies phase boundaries via spectral gap, relaxation timescales, and slow manifold dimension.
Partial-transpose negativity across all bipartitions classifies steady-state quantum correlations as separable, bipartite-entangled, or genuinely multipartite entangled (GME).
Quantum discord and quantum fraction metrics distinguish genuinely quantum collective phenomena from classical analogues. Amplitude and phase synchronization order parameters characterize coherence.
All steady states under local decay exhibit trivial synchronization (zero discord, zero mutual information) across all coupling strengths and dissipation rates tested.
| Topology | Dissipation | Coupling | Spectral Gap | Steady States | Max Negativity | Entanglement | GME |
|---|
| Channel | Coupling g | Spectral Gap | Max Negativity | Entanglement Type | GME |
|---|
Graph-correlated dissipation uniquely enables genuinely multipartite entanglement with maximum negativity of 0.387, while local decay, dephasing, and collective decay produce exclusively separable steady states across the full coupling range. The dissipation channel, not coherent coupling, determines the non-classical character.
The spectral gap under local decay remains constant at 0.050 regardless of coupling strength (0.01 to 3.0) or network topology (chain, ring, star, complete). This reflects the topology-independent nature of local dissipation, with a fixed relaxation timescale of 20 time units.
Under collective decay, spectral gaps span five orders of magnitude, from 5.25e-5 (chain, g=0.1) down to 3.62e-10 (chain, g=2.0). Star topologies exhibit the largest gaps among collective decay channels, reflecting constructive interference in highly connected networks.
All 100 parameter combinations (25 couplings x 4 dissipation rates) under local decay yield trivial synchronization: zero amplitude/phase synchronization, zero quantum discord, and zero mutual information, indicating complete steady-state decoherence.