Higher-order quantum processes respecting closed labs in a spacetime have quantum controlled causal order
Summarize this article with:
Quantum Physics arXiv:2605.08351 (quant-ph) [Submitted on 8 May 2026] Title:Higher-order quantum processes respecting closed labs in a spacetime have quantum controlled causal order Authors:Matthias Salzger, V. Vilasini View a PDF of the paper titled Higher-order quantum processes respecting closed labs in a spacetime have quantum controlled causal order, by Matthias Salzger and V. Vilasini View PDF HTML (experimental) Abstract:In quantum causality and quantum information, there is a vast landscape of abstract quantum protocols permitting cyclic or non-acyclic causal structures between operations, including frameworks for indefinite causal order and higher-order quantum processes such as process matrices. A longstanding open question is what is the largest class of abstract processes that admit physical realisations without post-selection. In this work, we provide a rigorous answer using a top-down approach grounded in relativistic causality principles. Building on the framework of causal boxes, which characterise the most general quantum information-processing protocols compatible with fixed background spacetimes, we formalise additional constraints (Acting Once + Local Order) capturing the closed-laboratory assumptions of the process matrix framework at a fine-grained spacetime level. We prove that any protocol in a classical acyclic spacetime satisfying these conditions is behaviourally equivalent to a quantum circuit with quantum control of causal order (QC-QC), providing a top-down derivation of QC-QCs from physical principles. Our results show that QC-QCs constitute precisely the class of higher-order quantum processes, including those with indefinite order, that can be physically realised within classical spacetime, ruling out more general non-causal processes under the closed-labs assumption. This clarifies the relationship between abstract higher-order process matrix frameworks and experimentally accessible quantum protocols, as well as the interplay between coarse-grained cyclic and fine-grained acyclic operational causal structures. We also develop characterisation techniques for process box protocols that lead to new causality-based open questions concerning spacetime quantum protocols and relativistic quantum experiments. Comments: Subjects: Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc) Cite as: arXiv:2605.08351 [quant-ph] (or arXiv:2605.08351v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.08351 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Matthias Salzger [view email] [v1] Fri, 8 May 2026 18:01:12 UTC (464 KB) Full-text links: Access Paper: View a PDF of the paper titled Higher-order quantum processes respecting closed labs in a spacetime have quantum controlled causal order, by Matthias Salzger and V. VilasiniView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: gr-qc References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)