{"paper":{"title":"How long can it take for a quantum channel to forget everything?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Andre Ahlbrecht, Florian Richter, Reinhard F. Werner","submitted_at":"2012-05-03T12:24:48Z","abstract_excerpt":"We investigate quantum channels, which after a finite number $k$ of repeated applications erase all input information, i.e., channels whose $k$-th power (but no smaller power) is a completely depolarizing channel. We show that on a system with Hilbert space dimension $d$, the order is bounded by $k\\leq d^2-1$, and give an explicit construction scheme for such channels. We also consider strictly forgetful memory channels, i.e., channels with an additional input and output in every step, which after exactly $k$ steps retain no information about the initial memory state. We establish an explicit "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0693","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":""},"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"}