Minimal operational theories: classical theories with quantum features

• URL: http://arxiv.org/abs/2408.01368v1
• Date: Fri, 2 Aug 2024 16:24:09 GMT
• Title: Minimal operational theories: classical theories with quantum features
• Authors: Davide Rolino, Marco Erba, Alessandro Tosini, Paolo Perinotti,
• Abstract summary: We show that almost all minimal theories with conditioning satisfy two quantum no-go theorems. As a relevant example, we construct a minimal toy-theory with conditioning where all systems are classical.
• Score: 41.94295877935867
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a class of probabilistic theories where the dynamics of each system is limited to the minimal set of operations consistent with the set of states and allowing for conditional tests. We show that almost all minimal theories with conditioning satisfy two quantum no-go theorems: no-information without disturbance and no-broadcasting. As a relevant example, we construct a minimal toy-theory with conditioning where all systems are classical. The theory does not have incompatible measurements nor preparation uncertainty relations, and it is Kochen-Specker noncontextual, and at the same time it exhibits irreversibility of measurement disturbance, no-information without disturbance and no-broadcasting. This proves that the latter three properties cannot be understood $per se$ as signatures of non-classicality.

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