{"ID":23586786,"CreatedAt":"2026-09-18T05:25:32.833479871Z","UpdatedAt":"2026-09-18T05:25:32.833479871Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20774","arxiv_id":"2609.20774","title":"All causally separable quantum processes are quantum circuits with classical control of causal order","abstract":"The concept of causal (non)separability describes whether the causal order between parties that perform local quantum operations is well-defined or indefinite. Causal (non)separability in the general multipartite setting was introduced and studied in [Oreshkov and Giarmatzi, New J. Phys. 18, 093020 (2016); Wechs, Abbott, and Branciard, New J. Phys. 21, 013027 (2019)]. We resolve an open problem from these earlier works by showing -- using a novel \"coherent teleportation technique\" -- that a sufficient condition for causal separability identified in [Wechs, Abbott, and Branciard, New J. Phys. 21, 013027 (2019)] is also necessary, and thus provides a complete characterisation of multipartite causal separability. A consequence of this result is that all causally separable processes admit a realisation as generalised quantum circuits in which the order between the operations is classically controlled, known as \"quantum circuits with classical control of causal order\".","short_abstract":"The concept of causal (non)separability describes whether the causal order between parties that perform local quantum operations is well-defined or indefinite. Causal (non)separability in the general multipartite setting was introduced and studied in [Oreshkov and Giarmatzi, New J. Phys. 18, 093020 (2016); Wechs, Abbot...","url_abs":"https://arxiv.org/abs/2609.20774","url_pdf":"https://arxiv.org/pdf/2609.20774v1","authors":"[\"Julian Wechs\",\"Alastair A. Abbott\",\"Cyril Branciard\"]","published":"2026-09-17T17:47:21Z","proceeding":"quant-ph","tasks":"[\"quant-ph\"]","methods":"[]","has_code":false}