No-go theorems on simulating uncertainty principle's signatures

Quantum Physics [Submitted on 4 Jun 2026] No-go theorems on simulating uncertainty principle's signatures Chung-Yun Hsieh, Minjeong Song, Shin-Liang Chen Uncertainty principle, one of the most iconic features of quantum mechanics, was originally viewed as a fundamental limitation. Since the inception of quantum information science, researchers began to use it to achieve quantum advantages. To better understand the origin of these advantages, an essential question is: To what extent can the uncertainty principle's signatures be simulated by a single measurement? As a single measurement clearly cannot demonstrate the uncertainty principle, such a simulation, if exists, implies the claimed advantages may either stem from other quantum features, or just be reproducible in a less resourceful way. In this work, we report a series of noise-robust no-go theorems, showing that strong enough signatures of uncertainty principle cannot be simulated by a single measurement, even when assisted by quantum pre- or post-processing. This signature is modelled by complementary instruments. We completely characterise complementary instruments by a numerically feasible measure and show that they are necessary and sufficient resources for the advantage in an operational task that aims to unambiguously send classical information. Comments: 5+10 pages, 2 figures Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.05884 [quant-ph]   (or arXiv:2606.05884v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2606.05884 Focus to learn more Submission history From: Chung-Yun Hsieh [view email] [v1] Thu, 4 Jun 2026 08:54:01 UTC (166 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-06 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)