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arXiv · 2606.05884

No-go theorems on simulating uncertainty principle's signatures

Chung-Yun Hsieh·Minjeong Song·Shin-Liang Chen
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Abstract

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.

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Chung-Yun Hsieh, Minjeong Song, Shin-Liang Chen. 2026-06-04. No-go theorems on simulating uncertainty principle's signatures. https://arxiv.org/abs/2606.05884

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