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arXiv · 2308.02252

Measurement incompatibility cannot be stochastically distilled

Huan-Yu Ku·Chung-Yun Hsieh·Costantino Budroni
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Abstract

We show that the incompatibility of a set of measurements cannot be increased 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. Expanding these ideas to Einstein-Podolsky-Rosen steering experiments, we are able to solve the problem of the maximum steerability obtained with respect to the most general local filters in a way that allows for an explicit calculation of the filter operation. Moreover, our results generalize to nonphysical maps, i.e., positive but not completely positive linear maps.

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Huan-Yu Ku, Chung-Yun Hsieh, Costantino Budroni. 2023-08-04. Measurement incompatibility cannot be stochastically distilled. https://arxiv.org/abs/2308.02252

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