arXiv subjects
Publications and source records attributed to Davide Rolino.
We propose an operational definition of complementarity, pinning down the concept originally introduced by Bohr. Two properties of a system are considered complementary if they cannot be simultaneously well defined. We further show that, within quantum theory, this notion is equivalent to the incompatibility of operations -- that is, their inability to be performed simultaneously.
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 $\textit{per se}$ 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.
The core of Heisenberg's heuristic argument for the uncertainty principle, involving the famous $γ$-ray microscope $\textit{Gedankenexperiment}$, hinges upon the existence of measurements that irreversibly alter the state of the system on which they are acting, causing an irreducible disturbance on subsequent measurements. The argument was put forward to justify measurement incompatibility in quantum theory, namely, the existence of measurements that cannot be performed jointly$-$a feature that is now understood to be different from irreversibility of measurement disturbance, though related to it. In this article, on the one hand, we provide a compelling argument showing that measurement incompatibility is indeed a sufficient condition for irreversibility of measurement disturbance; while, on the other hand, we exhibit a toy theory, termed the minimal classical theory (MCT), that is a counterexample for the converse implication. This theory is classical, hence it does not have complementarity nor preparation uncertainty relations, and it is both Kochen-Specker and generalised noncontextual. However, MCT satisfies not only irreversibility of measurement disturbance, but also the properties of no-information without disturbance and no-broadcasting, implying that these cannot be understood $\textit{per se}$ as signatures of nonclassicality.