Abstract
Based on an intuitive generalization of the Leibniz principle of `the identity of indiscernibles', we introduce a novel ontological notion of classicality, called bounded ontological distinctness. Formulated as a principle, bounded ontological distinctness equates the distinguishability of a set of operational physical entities to the distinctness of their ontological counterparts. Employing three instances of two-dimensional quantum preparations, we demonstrate the violation of bounded ontological distinctness or excess ontological distinctness of quantum preparations, without invoking any additional assumptions. Moreover, our methodology enables the inference of tight lower bounds on the extent of excess ontological distinctness of quantum preparations. Similarly, we demonstrate excess ontological distinctness of quantum transformations, using three two-dimensional unitary transformations. However, to demonstrate excess ontological distinctness of quantum measurements, an additional assumption such as outcome determinism or bounded ontological distinctness of preparations is required. Moreover, we show that quantum violations of other well-known ontological principles implicate quantum excess ontological distinctness. Finally, to showcase the operational vitality of excess ontological distinctness, we introduce two distinct classes of communication tasks powered by excess ontological distinctness.
Highlights
Operational physical theories such as quantum theory serve to instruct experiments and make corresponding predictions
3.1.1 Bounded ontological distinctness for three preparations. We explore another implication of Bounded ontological distinctness for preparations (BODP) via the following proposition, wherein we employ BODP for a set of three preparations to arrive at an upper bound on operational average pairwise distinguishability of these preparations, which is violated by a prepare and measure fragment of quantum theory entailing a set of three pure two-dimensional preparations
The subsequent quantum violation of the consequences of such principles discards the ontological models that adhere to these constraints as plausible ontological explanations of the operational theory under consideration
Summary
We propose a novel notion of classicality, “bounded ontological distinctness". As the experimental tests of the consequences of these ontological principles allow us to extend the corresponding implications beyond the particular operational theory to Nature itself [MPK+16], such an ontological notion of classicality should be robust to experimental imperfections Such a notion should be operationally vital so that its quantum violation yields an advantage in computation, communication or information processing tasks. For four preparations, the distinguishability of a pair of disjoint two-preparation mixtures yields an upper-bound on the average distinguishability of the remaining disjoint pairs of twopreparation mixtures, valid in all operational theories that admit ontological models adhering to bounded ontological distinctness of preparations along with the preservation of convexity of operational preparations on the ontic level (Proposition 2) This forms a robust version of the preparation noncontextual inequality featured in [SBK+09], and is a direct implementation of the aforementioned suggestion of Spekkens in [Spe05] to employ an operational similarity condition instead of the zero-measure operational equivalence condition. We conclude by laying out certain implications of our results, key conceptual insights, and tentative avenues for future investigation
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