{"paper":{"title":"Coupling Does Not Reduce the Auxiliary-Mode Count for $1/|\\omega|$ Spectra in Passive Lindblad Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Qing-Ao Xiang, Xin-Yuan Yang, Ya-Ju Song, Yan Liu","submitted_at":"2026-08-05T07:15:44Z","abstract_excerpt":"Representing continuous environments by finitely many Markovian auxiliary modes is fundamental in non-Markovian open quantum systems, yet a critical question remains: at a fixed mode budget, can coherent intermode coupling reduce the spectral approximation error? We prove that intermode coupling offers no advantage when passive, number-conserving Gaussian Lindblad auxiliary networks approximate a $1/|\\omega|$ spectrum over a finite two-sided frequency band. For any mode budget $N$, the general coupled class and its uncoupled diagonal subclass share the same optimal error, which is exactly the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04539","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.04539/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}