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arXiv:2403.09807 · Physical Review Letters

Revealing Hidden Physical Nonclassicality with Non-negative Polynomials

Ties-A. Ohst, Benjamin Yadin, Birte Ostermann, Timo de Wolff, Otfried Gühne, H. Chau Nguyen

Published Jan 24, 2025• 4 citations
arXivHTMLPDF

Abstract

Understanding quantum phenomena that go beyond classical concepts is a focus of modern quantum physics. Here, we show how the theory of non-negative polynomials emerging around Hilbert's 17th problem, can be used to optimally exploit data capturing the nonclassical nature of light. Specifically, we show that non-negative polynomials can reveal nonclassicality in data even when it is hidden from standard detection methods up to now. Moreover, the abstract language of non-negative polynomials also leads to a unified mathematical approach to nonclassicality for light and spin systems, allowing us to map methods for one to the other. Conversely, the physical problems arising also inspire several mathematical insights into characterization of non-negative polynomials.

DOI
10.1103/physrevlett.134.030201

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A key aim of quantum foundations is to characterize the sense in which nature goes beyond classical physics. Understanding nonclassicality is one of our best avenues towards finding a satisfactory interpretation of quantum theory. By determining which classical principles cannot be satisfied in any empirically adequate physical theory, we begin to see which principles can be preserved, which in turn gives us insight into the ontology of the world. These insights then guide us in determining which questions to ask and which experiments to perform next. Furthermore, it is these nonclassical aspects of nature that give rise to new technologies such as the speed-ups of quantum computation or the security of quantum key distribution. \n \nThe gold standard for establishing that a phenomenon is truly nonclassical is to prove that it violates the principle of local causality or the principle of noncontextuality. Much of this thesis reports on my research relating to these two principles. This research primarily involves (i) finding new justifications for our notions of nonclassicality; (ii) refining their fundamental definitions; (iii) quantifying and characterizing their various manifestations; and (iv) finding applications where nonclassical phenomena act as resources for information processing. \n \nUltimately, all of this work on nonclassicality is woven together into a novel framework for physical theories introduced by myself, John Selby, and Rob Spekkens. Its main advantage over preexisting frameworks is that it maintains a clear distinction between which elements of a given physical theory directly describe causal processes, and which refer only to one’s inferences about causal processes. This clarifies a number of confusions in the literature which arose precisely because previous frameworks scrambled causal and inferential concepts. Furthermore, local causality and noncontextuality emerge in this framework as the assumptions that the causal and inferential structures (respectively) that are operationally observed must be respected in the underlying ontology. This work constitutes a first step in developing a new interpretation of quantum theory—the first interpretation designed to satisfy the spirit of both local causality and noncontextuality.
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