Minimal operational theories: classical theories with quantum features
We introduce a class of probabilistic theories, termed Minimal Strongly Causal Operational Probabilistic Theories, where system dynamics are constrained to the minimal set of operations consistent with the set of states and permitting conditional tests. Specifically, the allowed instruments are limi...
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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/ada850 |
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| author | Davide Rolino Marco Erba Alessandro Tosini Paolo Perinotti |
| author_facet | Davide Rolino Marco Erba Alessandro Tosini Paolo Perinotti |
| author_sort | Davide Rolino |
| collection | DOAJ |
| description | We introduce a class of probabilistic theories, termed Minimal Strongly Causal Operational Probabilistic Theories, where system dynamics are constrained to the minimal set of operations consistent with the set of states and permitting conditional tests. Specifically, the allowed instruments are limited to those derived from compositions of preparations, measurements, swap transformations, and conditional operations. We demonstrate that minimal theories with conditioning and a spanning set of non-separable states satisfy two quantum no-go theorems: no-information without disturbance and no-broadcasting. As a key example, we construct Minimal Strongly Causal Bilocal Classical Theory, a classical toy-theory that lacks incompatible measurements, preparation uncertainty relations, and is noncontextual (both Kochen–Specker and generalised), yet exhibits irreversibility of measurement disturbance, no-information without disturbance, and no-broadcasting. Therefore, the latter three properties cannot be understood per se as signatures of non-classicality. We further explore distinctions between a theory and its minimal strongly causal counterpart, showing that while the minimal strongly causal version of quantum theory diverges from full quantum theory, the same does not hold for classical theory. Additionally, we establish the pairwise independence of the properties of simpliciality, strong causality, and local discriminability. |
| format | Article |
| id | doaj-art-e5ee3492e1d047a4bdb89c88d9d34f3b |
| 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-e5ee3492e1d047a4bdb89c88d9d34f3b2025-02-04T14:57:14ZengIOP PublishingNew Journal of Physics1367-26302025-01-0127202300410.1088/1367-2630/ada850Minimal operational theories: classical theories with quantum featuresDavide Rolino0https://orcid.org/0009-0007-2192-6178Marco Erba1https://orcid.org/0000-0002-2172-592XAlessandro Tosini2https://orcid.org/0000-0001-8599-4427Paolo Perinotti3https://orcid.org/0000-0003-4825-4264Dipartimento di Fisica, QUIT Group, Università degli Studi di Pavia , via Bassi 6, Pavia 27100, Italy; Sezione di Pavia, INFN Gruppo IV , via Bassi 6, Pavia 27100, ItalyInternational Centre for Theory of Quantum Technologies (ICTQT), Uniwersytet Gdański , ul. Jana Bażyńskiego 1A, Gdańsk 80-309, PolandDipartimento di Fisica, QUIT Group, Università degli Studi di Pavia , via Bassi 6, Pavia 27100, Italy; Sezione di Pavia, INFN Gruppo IV , via Bassi 6, Pavia 27100, ItalyDipartimento di Fisica, QUIT Group, Università degli Studi di Pavia , via Bassi 6, Pavia 27100, Italy; Sezione di Pavia, INFN Gruppo IV , via Bassi 6, Pavia 27100, ItalyWe introduce a class of probabilistic theories, termed Minimal Strongly Causal Operational Probabilistic Theories, where system dynamics are constrained to the minimal set of operations consistent with the set of states and permitting conditional tests. Specifically, the allowed instruments are limited to those derived from compositions of preparations, measurements, swap transformations, and conditional operations. We demonstrate that minimal theories with conditioning and a spanning set of non-separable states satisfy two quantum no-go theorems: no-information without disturbance and no-broadcasting. As a key example, we construct Minimal Strongly Causal Bilocal Classical Theory, a classical toy-theory that lacks incompatible measurements, preparation uncertainty relations, and is noncontextual (both Kochen–Specker and generalised), yet exhibits irreversibility of measurement disturbance, no-information without disturbance, and no-broadcasting. Therefore, the latter three properties cannot be understood per se as signatures of non-classicality. We further explore distinctions between a theory and its minimal strongly causal counterpart, showing that while the minimal strongly causal version of quantum theory diverges from full quantum theory, the same does not hold for classical theory. Additionally, we establish the pairwise independence of the properties of simpliciality, strong causality, and local discriminability.https://doi.org/10.1088/1367-2630/ada850operational probabilistic theoriesgeneralised probabilistic theoriesoperational theoriesquantum informationnonclassicalityfoundations of quantum theory |
| spellingShingle | Davide Rolino Marco Erba Alessandro Tosini Paolo Perinotti Minimal operational theories: classical theories with quantum features New Journal of Physics operational probabilistic theories generalised probabilistic theories operational theories quantum information nonclassicality foundations of quantum theory |
| title | Minimal operational theories: classical theories with quantum features |
| title_full | Minimal operational theories: classical theories with quantum features |
| title_fullStr | Minimal operational theories: classical theories with quantum features |
| title_full_unstemmed | Minimal operational theories: classical theories with quantum features |
| title_short | Minimal operational theories: classical theories with quantum features |
| title_sort | minimal operational theories classical theories with quantum features |
| topic | operational probabilistic theories generalised probabilistic theories operational theories quantum information nonclassicality foundations of quantum theory |
| url | https://doi.org/10.1088/1367-2630/ada850 |
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