An operational characterization of finite-dimensional quantum theory

Abstract:A key goal in the foundations of quantum mechanics is to identify operational constraints characterizing physical theories. Bell inequalities do so for classical probability theory, while Tsirelson's bound provides a first step for quantum mechanics. Here, we address the dual question: Can one certify that all correlations predicted by quantum theory are actually realizable? In this work, we construct a finite number of two-body correlations such that the only probabilistic theory that (1) realizes them, and (2) does so in a way that is stable under iterated teleportation, is quantum theory. For $(\mathbb{C}^d)^{\otimes n}$, Condition (1) can be verified using $\operatorname{poly}(d,n)$ measurement settings. Condition (2) may be understood as a hierarchy of tests, one for each number $N$ of teleportation steps. There is thus a sense in which finite-dimensional quantum theory can be self-tested. In particular, one can certify the existence of Bell inequality violations larger than any that have been directly observed.

arXiv:2610.03694 [quant-ph]

(or arXiv:2610.03694v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.03694 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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