{"paper":{"title":"The quantum instrument monad","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.PL","math.CT","quant-ph"],"primary_cat":"cs.LO","authors_text":"Tobias Fritz","submitted_at":"2026-06-26T07:45:03Z","abstract_excerpt":"Monads are a ubiquitous structure in functional programming used for modelling computational effects. For example, the state monad models the effect of a computation interacting with a memory system. Here we introduce the quantum instrument monad $\\mathcal{I}_\\mathcal{A}$, which models the effect of a computation interacting with a quantum system with algebra of observables $\\mathcal{A}$. It can be thought of as a noncommutative generalization of the state monad.\n  We construct this quantum instrument monad in two versions: a finitary version on the category of sets and a measure-theoretic ver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27805","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/2606.27805/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"}