A de Finetti theorem for quantum causal structures
What does it mean for a causal structure to be `unknown'? Can we even talk about `repetitions' of an experiment without prior knowledge of causal relations? And under what conditions can we say that a set of processes with arbitrary, possibly indefinite, causal structure are independent an...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-02-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-02-11-1628/pdf/ |
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| _version_ | 1823858031567306752 |
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| author | Fabio Costa Jonathan Barrett Sally Shrapnel |
| author_facet | Fabio Costa Jonathan Barrett Sally Shrapnel |
| author_sort | Fabio Costa |
| collection | DOAJ |
| description | What does it mean for a causal structure to be `unknown'? Can we even talk about `repetitions' of an experiment without prior knowledge of causal relations? And under what conditions can we say that a set of processes with arbitrary, possibly indefinite, causal structure are independent and identically distributed? Similar questions for classical probabilities, quantum states, and quantum channels are beautifully answered by so-called "de Finetti theorems", which connect a simple and easy-to-justify condition – symmetry under exchange – with a very particular multipartite structure: a mixture of identical states/channels. Here we extend the result to processes with arbitrary causal structure, including indefinite causal order and multi-time, non-Markovian processes applicable to noisy quantum devices. The result also implies a new class of de Finetti theorems for quantum states subject to a large class of linear constraints, which can be of independent interest. |
| format | Article |
| id | doaj-art-25d10c7185804d82821c797ba93c3928 |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-25d10c7185804d82821c797ba93c39282025-02-11T16:37:23ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-02-019162810.22331/q-2025-02-11-162810.22331/q-2025-02-11-1628A de Finetti theorem for quantum causal structuresFabio CostaJonathan BarrettSally ShrapnelWhat does it mean for a causal structure to be `unknown'? Can we even talk about `repetitions' of an experiment without prior knowledge of causal relations? And under what conditions can we say that a set of processes with arbitrary, possibly indefinite, causal structure are independent and identically distributed? Similar questions for classical probabilities, quantum states, and quantum channels are beautifully answered by so-called "de Finetti theorems", which connect a simple and easy-to-justify condition – symmetry under exchange – with a very particular multipartite structure: a mixture of identical states/channels. Here we extend the result to processes with arbitrary causal structure, including indefinite causal order and multi-time, non-Markovian processes applicable to noisy quantum devices. The result also implies a new class of de Finetti theorems for quantum states subject to a large class of linear constraints, which can be of independent interest.https://quantum-journal.org/papers/q-2025-02-11-1628/pdf/ |
| spellingShingle | Fabio Costa Jonathan Barrett Sally Shrapnel A de Finetti theorem for quantum causal structures Quantum |
| title | A de Finetti theorem for quantum causal structures |
| title_full | A de Finetti theorem for quantum causal structures |
| title_fullStr | A de Finetti theorem for quantum causal structures |
| title_full_unstemmed | A de Finetti theorem for quantum causal structures |
| title_short | A de Finetti theorem for quantum causal structures |
| title_sort | de finetti theorem for quantum causal structures |
| url | https://quantum-journal.org/papers/q-2025-02-11-1628/pdf/ |
| work_keys_str_mv | AT fabiocosta adefinettitheoremforquantumcausalstructures AT jonathanbarrett adefinettitheoremforquantumcausalstructures AT sallyshrapnel adefinettitheoremforquantumcausalstructures AT fabiocosta definettitheoremforquantumcausalstructures AT jonathanbarrett definettitheoremforquantumcausalstructures AT sallyshrapnel definettitheoremforquantumcausalstructures |