Digitizing Micromaser Steady States: Entropy, Information Graphs, and Multipartite Correlations in Qubit Registers

We develop a digitization-based analysis workflow for characterizing the entropy and correlation structure of truncated bosonic quantum fields after embedding them into small qubit registers, and illustrate it on the steady state of a coherently pumped micromaser. The cavity field is truncated to 32 Fock levels and embedded into a five-qubit register via a Gray-code mapping of photon number to computational basis states, with binary encoding used as a benchmark. On this register we compute reduced entropies, mutual informations, bipartite negativities and Coffman-Kundu-Wootters three-tangles for all qubit pairs and triplets, and use the resulting patterns to define information graphs. The micromaser Liouvillian naturally supports trapping manifolds in Fock space, whose structure depends on the choice of interaction angle and on thermal coupling to the reservoir. We show that these manifolds leave a clear imprint on the digitized information graph: multi-block trapping configurations induce sparse, banded patterns dominated by a few two-qubit links, while trapping on a single 32-dimensional manifold or coupling to a thermally populated cavity leads to more delocalized and collectively shared correlations. The entropy and mutual-information profiles of the register provide a complementary view on how energy and information are distributed across qubits in different parameter regimes. Although the full micromaser dynamics can in principle generate higher-order entanglement, we focus here on well-defined measures of two- and three-party correlations and treat the emerging information graph as a structural probe of digitized field states. We expect the workflow to transfer to other bosonic fields encoded in small qubit registers, and outline how the resulting information-graph view can serve as a practical diagnostic in studies of driven-dissipative correlation structure.