Abstract
We show that the quantum advantages arising from incompatibility of a set of measurements cannot be enhanced by subjecting them to a filter, namely, by combining them with a device that post-selects the incoming states on a fixed outcome of a stochastic transformation. This result holds for several measures of incompatibility, such as those based on robustness and convex weight. As an application, we show that, for Einstein-Podolsky-Rosen steering, our no-go results determine the maximum steerability attainable under the most general local filters, together with an explicit expression for the optimal filter. Moreover, our results generalize to nonphysical maps, i.e., positive but not completely positive linear maps.
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Acknowledgements
The authors acknowledge fruitful discussions with Joonwoo Bae, Jessica Bavaresco, Shin-Liang Chen, Máté Farkas, Erkka Haapasalo, Yeong-Cherng Liang, Simon Milz, Miguel Navascués, Bartosz Regula, Yen-An Shih, Anthony Short, Paul Skrzypczyk, Ryuji Takagi, and Hao-Cheng Weng. This work is supported by the Ministry of Science and Technology, Taiwan, (Grants No. MOST 112-2112-M-003-020-MY3), the Higher Education Sprout Project of National Taiwan Normal University (NTNU) the Ministry of Education (MOE) in Taiwan, the Royal Society through Enhanced Research Expenses (NFQI), the ERC Advanced Grant (FLQuant), and the Leverhulme Trust Early Career Fellowship (“Quantum complementarity: a novel resource for quantum science and technologies” with Grant No. ECF-2024-310).
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Ku, HY., Hsieh, CY. & Budroni, C. No-go theorems on probabilistically enhancing measurement incompatibility’s advantages. npj Quantum Inf (2026). https://doi.org/10.1038/s41534-026-01270-7
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DOI: https://doi.org/10.1038/s41534-026-01270-7
