Quantum Prescriptions Are More Ontologically Distinct Than They Are Operationally Distinguishable

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.

Featured image: This graphic is a schematic representation of the experimental fragments of quantum theory that are deemed nonclassical by various ontological notions of classicality. We introduce a novel ontological notion of classicality, termed, bounded ontological distinctness (BOD). We show that BOD can witness nonclassicality in experimental fragments that satisfy the other ontological notions of classicality.

Popular summary

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.

► BibTeX data

@article{Chaturvedi2020quantum, doi = {10.22331/q-2020-10-21-345}, url = {https://doi.org/10.22331/q-2020-10-21-345}, title = {Quantum prescriptions are more ontologically distinct than they are operationally distinguishable}, author = {Chaturvedi, Anubhav and Saha, Debashis}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {4}, pages = {345}, month = oct, year = {2020}<br /> }

► References

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Cited by

[1] Anubhav Chaturvedi, Máté Farkas, and Victoria J Wright, “Characterising and bounding the set of quantum behaviours in contextuality scenarios”, arXiv:2010.05853.

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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

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Quantum prescriptions are more ontologically distinct than they are operationally distinguishable

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