Quantum prescriptions are more ontologically distinct than they are operationally distinguishable

Anubhav Chaturvedi1,2 and Debashis Saha1,3

1Institute of Theoretical Physics and Astrophysics, National Quantum Information Centre, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-952 Gdańsk, Poland
2International Centre for Theory of Quantum Technologies (ICTQT), University of Gdansk, 80-308 Gdańsk, Poland
3Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland

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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.

For a set of physical entities, their distinguishability quantifies how well we can tell them apart employing a given physical theory. On the other hand, their distinctness quantifies how distinct these entities actually are (in reality). In classical theories, and in general classical thought, when it comes to sets of physical entities, distinguishability is synonymous to distinctness, i.e., what you see is what you get. However, in the work, we demonstrate that this is not the case for quantum physical entities. Quantum theory posits sets of physical entities that must be more distinct than they are distinguishable.

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