Mapping indefinite causal order processes to composable quantum protocols in a spacetime
Formalisms for higher order quantum processes provide a theoretical formalisation of quantum processes where the order of agents’ operations need not be definite and acyclic, but may be subject to quantum superpositions. This has led to the concept of indefinite causal structures (ICS) which have ga...
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IOP Publishing
2025-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/ad9d6f |
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| author | Matthias Salzger V Vilasini |
| author_facet | Matthias Salzger V Vilasini |
| author_sort | Matthias Salzger |
| collection | DOAJ |
| description | Formalisms for higher order quantum processes provide a theoretical formalisation of quantum processes where the order of agents’ operations need not be definite and acyclic, but may be subject to quantum superpositions. This has led to the concept of indefinite causal structures (ICS) which have garnered much interest. However, the interface between these information-theoretic approaches and spatiotemporal notions of causality is less understood, and questions relating to the physical realisability of ICS in a spatiotemporal context persist despite progress in their information-theoretic characterisation. Further, previous work suggests that composition of processes is not so straightforward in ICS frameworks, which raises the question of how this connects with the observed composability of physical experiments in spacetime. To address these points, we compare the formalism of quantum circuits with quantum control of causal order (QC-QC), which models an interesting class of ICS processes, with that of causal boxes, which models composable quantum information protocols in spacetime. We incorporate the set-up assumptions of the QC-QC framework into the spatiotemporal perspective and show that every QC-QC can be mapped to a causal box that satisfies these set up assumptions and acts on a Fock space while reproducing the QC-QC’s behaviour in a relevant subspace defined by the assumptions. Using a recently introduced concept of fine-graining, we show that the causal box corresponds to a fine-graining of the QC-QC, which unravels the original ICS of the QC-QC into a set of quantum operations with a well-defined and acyclic causal order, compatible with the spacetime structure. Our results also clarify how the composability of physical experiments is recovered, while highlighting the essential role of relativistic causality and the Fock space structure. |
| format | Article |
| id | doaj-art-d8e45f72f23b475fb3f53bd3757135c8 |
| institution | Kabale University |
| issn | 1367-2630 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IOP Publishing |
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| series | New Journal of Physics |
| spelling | doaj-art-d8e45f72f23b475fb3f53bd3757135c82025-01-31T12:17:58ZengIOP PublishingNew Journal of Physics1367-26302025-01-0127202300210.1088/1367-2630/ad9d6fMapping indefinite causal order processes to composable quantum protocols in a spacetimeMatthias Salzger0https://orcid.org/0000-0002-8021-0993V Vilasini1https://orcid.org/0000-0002-7035-4205International Centre for Theory of Quantum Technologies, University of Gdańsk , 80-309 Gdańsk, Poland; Institute for Theoretical Physics , ETH Zurich, 8093 Zürich, SwitzerlandInstitute for Theoretical Physics , ETH Zurich, 8093 Zürich, Switzerland; Université Grenoble Alpes , Inria, 38000 Grenoble, FranceFormalisms for higher order quantum processes provide a theoretical formalisation of quantum processes where the order of agents’ operations need not be definite and acyclic, but may be subject to quantum superpositions. This has led to the concept of indefinite causal structures (ICS) which have garnered much interest. However, the interface between these information-theoretic approaches and spatiotemporal notions of causality is less understood, and questions relating to the physical realisability of ICS in a spatiotemporal context persist despite progress in their information-theoretic characterisation. Further, previous work suggests that composition of processes is not so straightforward in ICS frameworks, which raises the question of how this connects with the observed composability of physical experiments in spacetime. To address these points, we compare the formalism of quantum circuits with quantum control of causal order (QC-QC), which models an interesting class of ICS processes, with that of causal boxes, which models composable quantum information protocols in spacetime. We incorporate the set-up assumptions of the QC-QC framework into the spatiotemporal perspective and show that every QC-QC can be mapped to a causal box that satisfies these set up assumptions and acts on a Fock space while reproducing the QC-QC’s behaviour in a relevant subspace defined by the assumptions. Using a recently introduced concept of fine-graining, we show that the causal box corresponds to a fine-graining of the QC-QC, which unravels the original ICS of the QC-QC into a set of quantum operations with a well-defined and acyclic causal order, compatible with the spacetime structure. Our results also clarify how the composability of physical experiments is recovered, while highlighting the essential role of relativistic causality and the Fock space structure.https://doi.org/10.1088/1367-2630/ad9d6fprocess matrixcausal boxcausal inequalitiesphysical implementations of processescomposability of processesphysicality of processes |
| spellingShingle | Matthias Salzger V Vilasini Mapping indefinite causal order processes to composable quantum protocols in a spacetime New Journal of Physics process matrix causal box causal inequalities physical implementations of processes composability of processes physicality of processes |
| title | Mapping indefinite causal order processes to composable quantum protocols in a spacetime |
| title_full | Mapping indefinite causal order processes to composable quantum protocols in a spacetime |
| title_fullStr | Mapping indefinite causal order processes to composable quantum protocols in a spacetime |
| title_full_unstemmed | Mapping indefinite causal order processes to composable quantum protocols in a spacetime |
| title_short | Mapping indefinite causal order processes to composable quantum protocols in a spacetime |
| title_sort | mapping indefinite causal order processes to composable quantum protocols in a spacetime |
| topic | process matrix causal box causal inequalities physical implementations of processes composability of processes physicality of processes |
| url | https://doi.org/10.1088/1367-2630/ad9d6f |
| work_keys_str_mv | AT matthiassalzger mappingindefinitecausalorderprocessestocomposablequantumprotocolsinaspacetime AT vvilasini mappingindefinitecausalorderprocessestocomposablequantumprotocolsinaspacetime |