{"paper":{"title":"On the Kolmogorov--Wiener--Masani spectrum of a multi-mode weakly stationary quantum process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.ST","stat.TH"],"primary_cat":"quant-ph","authors_text":"K. R. Parthasarathy, Ritabrata Sengupta","submitted_at":"2016-05-20T10:40:18Z","abstract_excerpt":"We introduce the notion of a $k$-mode weakly stationary quantum process $\\varrho$ based on the canonical Schr\\\"odinger pairs of position and momentum observables in copies of $L^2(\\mathbb{R}^k)$, indexed by an additive abelian group $D$ of countable cardinality. Such observables admit an autocovariance map $\\widetilde{K}$ from $D$ into the space of real $2k \\times 2k$ matrices. The map $\\widetilde{K}$ on the discrete group $D$ admits a spectral representation as the Fourier transform of a $2k \\times 2k$ complex Hermitain matrix-valued totally finite measure $\\Phi$ on the compact character grou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06278","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}